Question
A sum of money lent out at simple interest amounts to Rs. 1240 in 4 years and Rs 1360 in 6 years. Find the sum and rate percent?
Hint:
Frame 2 equations from the information provided and find the ratios.
The correct answer is: 1000 Rupees.
Complete step by step solution:
Let the sum of money = P and rate of interest = R
Case Ⅰ
We calculate simple interest by the formula, ![S I equals fraction numerator P T R over denominator 100 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAjCAYAAAApF3xtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAnZJREFUeNrtWkFERFEU/cZIizEkSZI2GUmLaJFZtIiMZCQxMtIi0apFi0iSkURapUUkGUmGMVq0aJOkRTKbpFUirVrMplXGGDHdmxvf9d7/7/8a5r3f4Szm/TM3He/de/4zltX4qABrxA9gHjgCDAGrtmciVknHa70Bi8ALYJulIXqAD7bPTcBR4Cuwj2ljTOtWC7EF3NHRmEngqWB9HrjM1qYkWqda08CsjsZkBAYgtoGLbG1DonWqhd9Z0tEY7CcTbA17wjOwla0XBFqnWlHgE7BdR2PQgA7b50HgLTVfjhemldUKA8eA98CUjqbgNPmkKfJOhmxK/vkwTSyVWj8ctjTFEPBaURt30fJacV2nESLtYWK4aUXPL4HdOhqzB1zwoJ33WAt3zbGOxpwBx/9IK3t+JQiKQoRptr9RfC5SB+cos6hdD2DDbf4jrex5nF4LXHFOCTFEheZo/vNo/WgFCJgNcooxPRckY2bozKnE9JUgGdNFvSPvkiDztGtEqClQSwzQrsEUuS5psBitO62AIk27B2N4hEXrcp3+Zq1B6Ao05IR2jmpMN/YoccwCj3zGdKOBOybpM6YbgX3gKrDXdomTocsfvzHdCPTT7sDXALxZv5O8lHmJ6f+oI2LU/J1u/6O044vEA1rzq9Omxy24TDPMXfa73KQkwavqtILMmBQNBI5dmqBedcYYg8MhIXkhLvjQGWMMDoMmwTqulXzojDHm0+E7VR+6QBhT8aEzxpiS5Ig0syOiqjOq+YrupBOC5quiM8YY/IXDoWA9y8awqs4YYyy6BsFfLITpuKwBb36h08YQt/ucFroawSZapqgf+YXuG19cOuNRd4HmVQAAAKN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+UzwvbWk+PG1pPkk8L21pPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1pPlA8L21pPjxtaT5UPC9taT48bWk+UjwvbWk+PC9tcm93Pjxtbj4xMDA8L21uPjwvbWZyYWM+PC9tYXRoPvvMkfAAAAAASUVORK5CYII=)
where P is Principal amount, T is number of years and R is rate of interest
We are given T = 4.
So, Simple interest for 4 years = ![S I equals fraction numerator P cross times 4 cross times R over denominator 100 end fraction](data:image/png;base64,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)
Formula for total amount = A = P + SI,
where A is the total amount, P is the principal amount and SI is simple interest .
We have A = 1240 and
.
On substitution, we get
…(i)
Case Ⅱ
We calculate simple interest by the formula, ![S I equals fraction numerator P T R over denominator 100 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAjCAYAAAApF3xtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAnZJREFUeNrtWkFERFEU/cZIizEkSZI2GUmLaJFZtIiMZCQxMtIi0apFi0iSkURapUUkGUmGMVq0aJOkRTKbpFUirVrMplXGGDHdmxvf9d7/7/8a5r3f4Szm/TM3He/de/4zltX4qABrxA9gHjgCDAGrtmciVknHa70Bi8ALYJulIXqAD7bPTcBR4Cuwj2ljTOtWC7EF3NHRmEngqWB9HrjM1qYkWqda08CsjsZkBAYgtoGLbG1DonWqhd9Z0tEY7CcTbA17wjOwla0XBFqnWlHgE7BdR2PQgA7b50HgLTVfjhemldUKA8eA98CUjqbgNPmkKfJOhmxK/vkwTSyVWj8ctjTFEPBaURt30fJacV2nESLtYWK4aUXPL4HdOhqzB1zwoJ33WAt3zbGOxpwBx/9IK3t+JQiKQoRptr9RfC5SB+cos6hdD2DDbf4jrex5nF4LXHFOCTFEheZo/vNo/WgFCJgNcooxPRckY2bozKnE9JUgGdNFvSPvkiDztGtEqClQSwzQrsEUuS5psBitO62AIk27B2N4hEXrcp3+Zq1B6Ao05IR2jmpMN/YoccwCj3zGdKOBOybpM6YbgX3gKrDXdomTocsfvzHdCPTT7sDXALxZv5O8lHmJ6f+oI2LU/J1u/6O044vEA1rzq9Omxy24TDPMXfa73KQkwavqtILMmBQNBI5dmqBedcYYg8MhIXkhLvjQGWMMDoMmwTqulXzojDHm0+E7VR+6QBhT8aEzxpiS5Ig0syOiqjOq+YrupBOC5quiM8YY/IXDoWA9y8awqs4YYyy6BsFfLITpuKwBb36h08YQt/ucFroawSZapqgf+YXuG19cOuNRd4HmVQAAAKN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+UzwvbWk+PG1pPkk8L21pPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1pPlA8L21pPjxtaT5UPC9taT48bWk+UjwvbWk+PC9tcm93Pjxtbj4xMDA8L21uPjwvbWZyYWM+PC9tYXRoPvvMkfAAAAAASUVORK5CYII=)
Here we have T = 6.
So, Simple interest for 6 years = SI = ![fraction numerator P cross times 6 cross times R over denominator 100 end fraction](data:image/png;base64,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)
Formula for total amount = A = P + SI,
We have A = 1360 and SI =
.
On substitution, we get A = 1360 = p +
…(ii)
Form (i) and (ii), we have
![fraction numerator 1360 over denominator open parentheses 1 plus fraction numerator 6 R over denominator 100 end fraction close parentheses end fraction equals fraction numerator 1240 over denominator open parentheses 1 plus fraction numerator 4 R over denominator 100 end fraction close parentheses end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAAAxCAYAAACRbJggAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABYBJREFUeNrtXWFkVlEYPvKZTyYySSaRzCTTn2QyE0lmMuOTmUnGfiTpXz+SfiTSr0nGTJL+TWZmpj8zk2Qkk2RG0o9+TEwy85nx9b72fjo7O+eec7b73Xvuve/Dy3fvOfd8O+9z9p73Pee89xOi8WgDeQiybCi/DDIHsglSBVkFGQVpMdS/ADIJ8pfqz4B0K3WOgIyBLJGM070iw8bDJZC3pNctqjfo0G4vSM1Qljse3oCMRHR4AaQfpEm6dx7knabuCA3eNklZqPD3Sr15kOuKwucLPphtPCyCDIA00/VZkA90zwSs+y2izdzyUPOs/1e5RuV+cniuAvJcc3/UQkxR4MPDKZAvEeVoaYcNbeaaBx8lngZZ0SjORQk4VV41uDNveSx7G5VqhFsyH9FmrnlwUeJxkFvkN/coZTi4Tzi0sa64LHXgvTUey16DuZNcDZ0uv5DlNrWZax5qljJZ7hksBPrKUxQsbpHboQYp2xHfs8Vj2Xkwlylou6Qpewpyx9JmrnlwUeJRkD5SYrfm+c9ksUsgh0jRaMVvOyqxymPZmYdpg5vQobHWvoO5WhSLUI+SlzQBYaumLq58/JKu1wzTW5ndDCceTtNAPmMoX9KU6drMNQ8HDTzmyBrbpi0MLq5p6lzlANDKQzvIBMhhD5dQlULw4DOYO8h9kIGuxA0DAbIV7ydCVLwSvDQXxQMG35PkwsXRZq55iFqsr0h+MC7d/AC5qYmCse6wpPCLFFVfUeouUBBZouce0LMMMw+zZBjibDN3PERNRYguUmSVBBXQa2jrGP23b1CAsUjP6wKYl9QernyMi/87W0UexFE8uLgOvoOZeWAwGAwGg8Fg+Pinvn4og8FguFkTlsZbV9ZrGDww2M1gMBgMBsMHuBWJ6S9FO9cwQP0uMQ/54cF0+ikU4PkM3NauGvzRR9J93AL/A/LMsW084TUVSD9D56GOQUNMkDoPeEjkScCKwyRXPLB/LqIOngTro894kAkPJWFKT6fjdzwW+syXJBE6D3UgDx8MgzlVHvBQD+bdlQNW3muhP2gkA4+SnlTurVD/XFCmNlpS6mMWeEDgoaKPYieBohYaD3hc72HgCvxN09pP6mhFKUcLsCldn6CprZIhXWSBh7obVLeytdB4WNH8J4UG9L3wSCi+DKaJPt9S/Om6j4bZKDP77FOr2JsskBSywMN9kCHpuqaJa1LjAbOglzNgDVbF7lSqZrLSciT8ij7jYF8Q+rw0F2ASQHvC/csKD7aNoVR5GBT6lJfQMEG+mpAUJb/1CJd0hqXroQNM2eOK9UlqZSALPOgGtwiFhwmHB2wv4ksCHRQEopuB65AvxO7lK1zOUV8m83GfU9xQCgMrKzzYBnOqPEwL+5qm7UV8SVqv72InfV0NKNY1qwBd1D9f9Ijk15yzxEPUYE6Vh69i5/0J+/nDG/VM2kgjCGQeYuBhQ7hvHxZFiWhZ/iT8ncxDDDxUG6yQrB6BrAb8fcyDAdusRC2SfuEf8xADD3Er8SCH1UPKWsj6YC4kDzy9sZuRGx448OAAMDc88JLQXvDSXEZ5cFmsL5oSQ900YR4scNlGTSvj2LZ9iy9dXCHp3Ue5CaFuZzMPFoR8wCVq+xbP02IKVQvJgtidyWArtw2swYT7yjzEwEMWjh7WDNOy/FsouP8/41EeBdQHHwHNKA+rQv8bIiErEX/3RD7ffEjs/nFMW3lIwR/zECMPoafr1BzvbXmUh6gL5iEGXbSIsBMpXSxCyWIRSg4WIe2EVuYhJh7uinBT3F18Nfw861GuwxPSQ5pgHmLiIdSXj5iiaIyMMZXqGEXMPR7lKrBsMpD+Mg8xAKeAkH6J3rau2kvT0brhP9lWXgf2d0yYf3swaTAPFvwDNW0Jd1wBJsgAAAF/dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xMzYwPC9tbj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtZnJhYz48bXJvdz48bW4+NjwvbW4+PG1pPlI8L21pPjwvbXJvdz48bW4+MTAwPC9tbj48L21mcmFjPjwvbXJvdz48L21mZW5jZWQ+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtbj4xMjQwPC9tbj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtZnJhYz48bXJvdz48bW4+NDwvbW4+PG1pPlI8L21pPjwvbXJvdz48bW4+MTAwPC9tbj48L21mcmFjPjwvbXJvdz48L21mZW5jZWQ+PC9tZnJhYz48L21hdGg+/eANkwAAAABJRU5ErkJggg==)
This can be written as ![fraction numerator 1360 over denominator left parenthesis 100 plus 6 R right parenthesis end fraction equals fraction numerator 1240 over denominator left parenthesis 100 plus 4 R right parenthesis end fraction](data:image/png;base64,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)
On cross multiplication, we get 13600 + 544R = 12400 + 744R
On rearranging the above equation, we get 200R = 1200
Divide on both sides by 200.
On dividing, we get R = 6%
Substitute R = 6% in (ii).
Then we get 1360 = p + ![fraction numerator P space cross times 6 cross times 6 over denominator 100 end fraction](data:image/png;base64,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)
![not stretchy rightwards double arrow 136000 equals 136 P](data:image/png;base64,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)
On simplifications, we get P = 1000.
So principal amount P = 1000 Rupees.
Related Questions to study
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Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x , Jaime could bicycle on the 4th week to meet his goal?
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![2 left parenthesis 5 x minus 20 right parenthesis minus left parenthesis 15 plus 8 x right parenthesis equals 7](data:image/png;base64,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)
What value of satisfies the equation above?
![2 left parenthesis 5 x minus 20 right parenthesis minus left parenthesis 15 plus 8 x right parenthesis equals 7](data:image/png;base64,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)
What value of satisfies the equation above?
A laboratory supply company produces graduated cylinders, each with an internal radius of 2 inches and an internal height between 7.75 inches and 8 inches. What is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?
A laboratory supply company produces graduated cylinders, each with an internal radius of 2 inches and an internal height between 7.75 inches and 8 inches. What is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?
In the xy-plane, the graph of
intersects the graph of y =x at the points (0,0) and (a, a). What is the value of a?
In the xy-plane, the graph of
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Snow fell and then stopped for a time. When the snow began to fall again, it fell at a faster rate than it had initially. Assuming that none of the snow melted during the time indicated, which of the following graphs could model the total accumulation of snow versus time?
Snow fell and then stopped for a time. When the snow began to fall again, it fell at a faster rate than it had initially. Assuming that none of the snow melted during the time indicated, which of the following graphs could model the total accumulation of snow versus time?
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The line with the equation
is graphed in the xy-plane. What is the x-coordinate of the x-intercept of the line?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOcAAACvCAYAAAAG/8khAAASfklEQVR4nO3dfVzV5f3H8deRowZygCx0GpsQqJnFErWVukRzbZW1eX+T2kxXak3rYbXUqNzPtQXiTct71zQNTVNTU2utQb/UQB1Tmoig4gRDxeTmnJSbc861PyzH5g1awLnO9f08Hw/+4HQ4Xp+u8z7X9f1+4fO1KaUUQgjtNPL1AIQQlybhFEJTEk4hNCXhFEJTEk4hNCXhFEJTEk4hNCXhFEJT9vp88ZjIqPp8eSHq1aGj+T799+s1nOD7AhtCTGSUJeoE69Sqw8Ii21ohNCXhFEJTEk4hNCXhFEJTEk4hNCXh9FeqjOzl05iytZAr/0FuNUVbZ/DM8s9x+c1f7npwZa/kmRe2UlTbmFUh216YxlvZZbX8f/A/Ek6/5CJv1XRmlPyCqfdHYLvicxvT6v4JDDuZzLOrDlDRQCP89hQVuWt47reljJz2U1pduTiwRfCzaQ9xcsrLrMp1NcgIG4qE0+8oqnPX8dLvAxk9Kg5HbW9eAFtzuo59hNDfJ/JO7tl6H+G1UK48dh0o+88D1Tm8k7CMkDGD6OQIuKrXsDm6MuapZiQmrCOv2pz1U8Lpd8r4x4Y1HBvxMN2bX92bF8DWvCsDRpxi8YbP0Saert3MHTKZtPJvPmEUZzPfZ/GxPgzo3qKWHUFNATTv/jDDj61hQ2ZZ7U/3ExJOf1N5mJ2byukeF0XQNf2gg7ZxsZzZ9Bk5lTqsLoqz+z5kWW5HOrVr9vVjLnJ2fsqZHnfQNujqowlAUBSdepSzeedhKut8rL5hSDgrKUpLZkjnwSRlnEZRSVHqH3go+l4S0op9Pbgrcx8nLfERuty3hAMeAA/OjGQe/O2O8yuc5yDLf3E3w1MO4QVU8RH2Hm9N2wjHJV/nzgdnkVHiOf/9//WnfedXSCvxAAGERNxMm+M5HCl2N3SV/+McRz9ayCuz1uNqdZr0ZfN5a8dx3OoMR/Z+QZt2NxHyX8+/mvl1ENGuNUV7j1Csw2dPHaj3361tCOrMbrblt2fgzz7gpbe380DVcdYc6cbvUu4lsGNzXw/vCs6St3YtB4PCced+Tm6xmw5hB1idvIKDIdGUA0EBzQi7MYjQoCbYAM+pQv5JS/pd37jG63g4syOV/M59uW/tG6za0ZOqAx9w5CcJrLjXwa1h57e/AdeH8wOOUXiqEiIaX2pADSSQyD596f7un8no/WumPhlLAIA7k8IsLz/oF0LNDfvVzW9jrg9vCVmFnPJAhAHvbANKAFvzHjw2WnE24wBzhr/GbyNe443n7iH8GndGDS+ItsOeJipzNkvIB85xZP0S1pxoApWlOL3Q8nQWn5wZyPiffv8Kx2ABNO85gtGUsmvgCka+PIub5s7i2btaXsNxWwM7d4ysnYHcM6w1tR05++/8fjeGbGsBbATe3JGujaDVbTHc6EcTZwsM5kY8VB19n5l/7cxLT3WFYyU4vcXsXJxG21eGcXvg+YICrm9JW85Q6rzU1jSYqNs70qi8Nbe1v+GiYHqdpRTzPVpc78tV8+uxHM8j0xlNhzY1tucBobRo14ji0q/wXvQTtc2vG2fpGWjXkms4T6Y1c8KpTrNrWSoVP27Chx/s5bQfHXec327uZdmru+nx4iDubNOGkPJ8stav4P32jzM2NuxC0Gwt23Cro4BDxy++pqdKdrH8Yxfdw3by4e5T/3NR3ovreD6HHTfTpmWTBqjqSjyUHT1Izk2x3NK6xlhszWnTMZTDh4q4qLpa59fF8UMFBHdsQws/+mC+Er/f1qrTmby3vZig438jte14Eu9pwf3D3+bt+5x8tbsZj73St/YL2VqopMXQ8Qy6OYhGrmY4PFtZuOd1NrwazX+tc0Ed6D0okOczDjMl/kaCcHM680N2fOnl+OZ/0Pa5l7mnxWOMXLaaPpVe9gQM5uWHf4CNcnIy9hA0aAqx13omtM5VUpibQ/X3Qsh5ayYZsaMZ96MbsRFK7L29CXp2NzlTe3JnkO3q5/fsYXZ9HMiAmR2u8Sy2xlQ9im4TWZ8vr5TyqPLtM9SP2vRQTyzLUk6vUqoqT6194h7VedBMlfpFRT3/++d95zqLNqhxj6aow1XeC98/8UCySj/jvsSTvarq4DI19K7pKvWMWyn1pdo+/T4VHTdBLd9fqrzKq6qOrFHj4u5Sg1/7m/qi+vxres/8TSXc9ahavN/5nYZaN3N6TuX+eZS6ped4Ne/TQlVd8z9VZatlgx9SCaknlfeq59etzqROV90GLVX7z3nrYHwN8d6tnZ+HUw8NXqe3RO2bN0YNXZylzl3VDzjV/sVj1dB5meff4N9B/dfqVs59C9XQwdcQtHNZavHgMWr+vhJVN9HU471rzjGnldjCiH18Ok+UrmZRxulafuHbQ0nGWywpHc6sx+8g2Nc72loFEBz7S2aNd7FkYToltf7i+2kyFq6mdPx0flXj2NwENqXq7y5jVuo345M61VnKyu2Ehl7pBI/CXVZOZUgozergndtwtXr4qvQsTcMctZwYqaKs1E1IWFCdBlOH967fnxCyNFsQoaG1Pgl7aKgfTnQAzcIctT+NJoSG+frsc/2Qba0QmpJwCqEpCacQmpJwCqEpCacQmpJwCqGper/OKYS/Mv46p68LbAg6XLBuKFapVYeFRba1QmhKwimEpiScQmhKwimEpiScQmhKwimEpiScQmjKkHC6OZ21iSWJ03j8/ngef6/Q1wNqOKqYrHVLSHrxVzzYaRIbT/i6m3t98eDKXsXT8R2JiYyiffxkUgy87V9NhoTTzo2xDzG6XzvKDpT7ejANyxZO7IAR/CKmmoO19vTwVwp3wRZmLKpg1NpMcna/zYQWHzM98S8UmloyRnVCsGF3hFJrYwAjNcYRFlL70/yWDXurXkx5NYjQZgFALD++uzXzM6pxKzCqcVANBoVTGM3uINQO4MGVn8p7++JZNHsAUYbs/S7F4NKEcVxZpDw/jPheE0n59CNWr99Fkdvcfa2EU/iP4FiGJ65hT/4+ts64nb1JCcxJPWHsSSEJp8Y8WfPoGRlFzEVfMfScl4XH1wOsK54s5veIuUSdUcT0mMfn/1uoLYR2/YfQP7SQ9NziS9z0yAxyzKmxgNgn+eTok74eRv0LiGXC9kNMuJaf8bip9EbT546IWm8h6K9k5RR+wE3xjsXMWPoZJ9wKlJMj27ZxYMhUxnXT+ebI340h4aykMO1NEpNTyKSczBWzSVyYRqGp+52avAWkLZzJrBXpQDork2eyKK3AsK2eDft1ARSuHEuPmLZ06ZvA5sCRLJ7W0+gb6MrtGOqAVeoE69SqQ52GrJxCmEfCKYSmJJxCaErCKYSmJJxCaEqaSgtxGb4+WytNpeuADqfdG4pVatVhYZFtrRCaknAKoSkJpxCaknAKoSkJpxCaknAKoSlDwllJ0fYFjIvvSExkDF0enMJqw3uaXqDKyE6ZTO/oKGIiO9J74iqyXcb0SKjBer2JDQinoiJ3HXM2X8ewP+9gb+oSHmu1nRcffYOdTrP+qvFiFRRsnMuSs0N552AOn70zjvAtSSRtO2bgB5P1ehMbEE4PTlc0oxNG0TMqjOCoeH45+qcEF+9gd95ZXw+unjWlVa9JzBjTlXB7U8I7d+fuEC+V1R4DwwlW601sQA8hO+FxPyK8xiMB9iY0CmhDRHgTn42qYdiwh4aen0TlJH/rFvb1TyZ5cLQJn7qWZ+AcfkXunj3Y+/ale4Tp4QTw4spaxW8G3stPJr7Jzo/XsSH9C0y9Y4qVGBZORfWRzcx67zZ+90IfWhncX+Y/GhEcO4zX1u0i759bmB6bzaxJC0gtlnj6O6PCqVyfszwxk15zJ9GnVVNfD6fB2YI70O+RBwj5cj95RVW+Hs7Vu9a+tRZhwDHn19zH+CBxLU0mvsjIW0OxKReFuWWEtbuJYEusoOd53FV4w7vww6jrfD2Uq/dt+tZagBkrp/s4ab9/hU3f78ltFYf5R+bf2bV1Ps+vzMNrcjDVSXa8nsjSjCLcgHLlsW1jAYNmj6Wbw4yptTIDVs4SMv/4DE/8aTceUvnowuM30GfOMBw+HFn9sxMY+C9ShnfjD54b6PDwo0x4Komp7UIMvCteJYVpb5Oy5QMyKYcVs0k88RDDH48nwtDPIelbWwesUidYp1Yd6jT0M0cI/yfhFEJTEk4hNCXhFEJTEk4hNCXhFEJT0lRaiMvw9aUUaSpdB3S4JtZQrFKrDguLbGuF0JSEUwhNSTiF0JSEUwhNSTiF0JSEUwhNGRJOD67sVTwd35GYyCjax08mxSpNpWtQJTtJerAfczJdvh5KPZCm0n5I4S7YwoxFFYxam0nO7reZ0OJjpif+hUIrpdOdz6aXp7Bof6WvR1JPpKm0H7Jhb9WLKa+OIi68KfbwWH58d2uoqMZtmXC6yF35JzJC2hHs66HUK2s1lTYgnIDdQWizAMCDKz+V9/bFs2j2AKLMqK4WHpx/X8Hcsp/zXL9bTeg7I75mztvXlUXK88OI7zWRlE8/YvX6XRRZYOlUJRksXApjHovDYV7jIEszJ5zBsQxPXMOe/H1snXE7e5MSmJN6wuyTQuoEn8xZQ5OxQ+nkCPD1aEQdMyec37CF0K7/EPqHFpKeW4y59xnz4tz5J15YvpE/DoijbWQUt/R/nVIO8Eb/22n/660U+3qI4jsx8xDF46bSG02fOyIwdz1phKP7NNKPTrvwiDtzNnf1/4gR69fwdJzZp4aswICV003xjsXMWPoZJ9wKlJMj27ZxYMhUxnVr7uvBCfGtGRBOG/brAihcOZYeMW3p0jeBzYEjWTytJ+GWOUFSyudr/8ir87fi5F9smj+TBWkFhm3pKylMe5PE5BQyKSdzxWwSF6ZRaFaR/0WaStcBq9QJ1qlVhzoNWDmFMJOEUwhNSTiF0JSEUwhNSTiF0JSEUwhNSVNpIS7D15dSpKl0HdDhmlhDsUqtOiwssq0VQlMSTiE0JeEUQlMSTiE0JeEUQlPmhVOdJiNxAHfOzsTt67E0BFVGdspkekdHERPZkd4TV5Ht8vh6VPXAer2JDQtnBQUbX+PX8zMN+1vGy6mgYONclpwdyjsHc/jsnXGEb0kiadsxw9601uxNbFA4FRW57zIrw86dDl+PpaE0pVWvScwY05Vwe1PCO3fn7hAvldUew8Jpzd7ExoRTOfewaI6Tkc/3J8bMzkiXYMMeGkozG6Cc5G/dwr7+ySQPjjZnYr9hwd7EZpSmTrNr4bswxootIr24slbxm4H38pOJb7Lz43VsSP/CzONti/UmNiCcboo/WcqixgN5LO56LNM26IJGBMcO47V1u8j75xamx2Yza9ICUosNjKfFehP7fzid6Sx8bin/P2cwnaKiiIkZwBslUDp3ALdET2ZbsYlnLi/NFtyBfo88QMiX+8krqvL1cOqPRXoT+//RmaMHCbsPkfDN9+5M5nQdwMpR60h/Js6AAq+Nx12FN7wLP4y6ztdDqV8W6E3s/yunlamT7Hg9kaUZRbgB5cpj28YCBs0eSzeHSVNrzd7EBs2gF1fWeub8bgGbysG5cQGvLjC7rynYCQz8FynDu3FLZBcenvohQWOTmNqjpWHH3tbsTSx9a+uAVeoE69SqQ50GrZxCmEXCKYSmJJxCaErCKYSmJJxCaErCKYSmJJxCaEqaSgtxGb6+zilNpeuADhesG4pVatVhYZFtrRCaknAKoSkJpxCaknAKoSkJpxCaknAKoSlDwukic/YDxERG/ecrejzvFhjcR+cbqpisdUtIevFXPNhpEhtPGNjYC7DiHBvSYsfJySM38dSS6dxzw9cdZRq3oF1EE98OqyHYwokdMIJA5w4WlZjahw6sOMdmhNNbzqmT0XTt3oW4IIP7VlxWYxxhIb4eRP2y4Bybsa2tLuVk5Q00b2qNSbMkC86xGeEsKeLQsTU82+v8HahiOg3hpXXZuEze5VmNBefYiG2tcvQiaffPCbXbwH2Kvy9+gRGTn6Hx91aR0N3c1olWYsU5NmLltDULPT9pAPYWdP7lGIY7DvPXvYX4c793T9Y8etY8O3nhK4ae87L8urZrZeocX4kRK+dFAuw0beT/3cADYp/kk6NP+noYejJkjq/EgJWzkqK0N5m7bi/F33QDf38zeweZ3Q3cWqw5xwaEMwB74zJ2zhjI3TFt6dL3JT4IGW18N/ALvAWkLZzJrBXpQDork2eyKK3AsJv7WHOOpeN7HbBKnWCdWnWo04CVUwgzSTiF0JSEUwhNSTiF0JSEUwhNSTiF0JQ0lRbiMnx9KaVewymE+PZkWyuEpiScQmhKwimEpiScQmhKwimEpiScQmhKwimEpiScQmhKwimEpiScQmjq36lmsrZamsM3AAAAAElFTkSuQmCC)
The table above shows some values of the functions w and t . For which value of x is
?
![](data:image/png;base64,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)
The table above shows some values of the functions w and t . For which value of x is
?
Solve each inequality and graph the solution :
![fraction numerator negative 3 x over denominator 8 end fraction minus 20 plus 2 x greater than 6](data:image/png;base64,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)
Note:
When we have an inequality with the symbols < or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
Solve each inequality and graph the solution :
![fraction numerator negative 3 x over denominator 8 end fraction minus 20 plus 2 x greater than 6](data:image/png;base64,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)
Note:
When we have an inequality with the symbols < or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
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)
The graph above shows the positions of Paul and Mark during a race. Paul and Mark each ran at a constant rate, and Mark was given a head start to shorten the distance he needed to run. Paul finished the race in 6 seconds, and Mark finished the race in 10 seconds. According to the graph, Mark was given a head start of how many yards?
![](data:image/png;base64,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)
The graph above shows the positions of Paul and Mark during a race. Paul and Mark each ran at a constant rate, and Mark was given a head start to shorten the distance he needed to run. Paul finished the race in 6 seconds, and Mark finished the race in 10 seconds. According to the graph, Mark was given a head start of how many yards?
Solve each inequality and graph the solution :
-2.1x+2.1<6.3
Note:
When we have an inequality with the symbols < or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
Solve each inequality and graph the solution :
-2.1x+2.1<6.3
Note:
When we have an inequality with the symbols < or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.