Question
A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for all 15 members of her family. If Aunt Ethel paid $375 for all the sweaters, what was the original price of each sweater?
The correct answer is: $45
- Hint:
○ Form the eqaution using given information.
○ Take variable value as any alphabet.
○ Take terms with cofficient at one side and without cofficients at another side.
- Step-by-step explanation:
○ Given:
Discount per sweater = $20.
No of sweaters brought = 15.
Total money paid = $375.
○ Step 1:
Let the original price of one sweater be x.
So,
Selling price of 1 sweater = original price - discount
Selling price of 1 sweater = x - 20
○ Step 2:
○ Total selling price.
As 1 sweater cost (x-20)
So, 15 sweater will cost
15(x - 20) = 15x - 300
As it is given total money paid is $375
∴ 15x - 300 = 375
15x = 375 + 300
15x = 675
x = ![675 over 15](data:image/png;base64,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)
x = 45
- Final Answer:
Hence, the original price of sweater is $45.
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Prove that ∠ ABC ≅ ∠ ADC
![](data:image/png;base64,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)
Prove that ∠ ABC ≅ ∠ ADC
![](data:image/png;base64,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)
A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?
A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?
Prove that ∠ ABC ≅ ∠ PQR
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)
Prove that ∠ ABC ≅ ∠ PQR
![](data:image/png;base64,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)
Show the conjecture is false by finding a counterexample. If
≅
, then point B is the midpoint of AB.
Show the conjecture is false by finding a counterexample. If
≅
, then point B is the midpoint of AB.
A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?
A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?
Use the Law of Detachment to make a valid conclusion in the true situation.
If the measure of an angle is less than 90°, then it is an acute angle.
![m straight angle Q equals 165 to the power of ring operator](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAAARCAYAAAAxMemoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAotJREFUeNrtmF9EZFEcx4+MZCR6SLLSW1ZWIlkray1rrR56iCQ9JLEPSQ+9rH1Y+xTpYR96WNY+rLUPMTJWMpYkycgykiRZkmStXpIkY8T0/fG9XGPOOXfmzJ07uzs/Pi/n3rnzu7/v+f05V6m6RW2L4Jos1sNRe+KkQQfZqSWRXtb1UTcUxrMOZlLk9hGsWMT7AW5BljvreYj+dIN3YN9y3wBIMIji1xp45rueN/DXCPQJXILHhrT/zmA0kGFwAQZD8ukbeG0IpOL1NYop1gImuHn8ArmUuHTUJe6rRZw5CljMJIN2Q/ZPF+AekHH4vU2kG2IU5z14A9rBMnfsHzDE663gAwMsafi2jF1qEqcTHDJjdHYFGiMQSDbNeEgCBbYERcrQmRjoAqdMv20wxvVO1uD2gM9etYgjtgBmLc/ZAH2awNhwEei4oFdEItAvsMlM8dtv8FmzbnNasiEZQBzF7Omy3HMG4hFkUJa9J8nBJceNPFHk9zlWmBSYB82VcKyBfxwvcd1ksRLECfq8q4h6kKzvsdzH6O8gN/WMxtd+ToaSfQ9dHZMAblVg3e/gekBxvPtt4+UIhwwVQYkT3x4UWe9jJbGd97ZdBZKe86UC64pNPFWCOJ7dWgaEtKb/VCODUgbfcgGem3V1bJlzvut6Ew+YpYrjjeBTmmsyMS5V4RigE2iGA1KhSen6aXnmI3Di6ljSN06Xux7nkFGOON7LnoNJljyxXo7nC1U6p+UNVUHK1LTPN3nHA/CiIC5PfAfsVxRnxNWxS+5+l/WtgL3AY8XQ27Ikr2nCYQhj61ltnGblQHlHwZ4W3DPKweGOMUrwi8g/a2M8LGe4e9tU3WrOmvmF40j9h1/A7wFfe84aLJweZQAAAK10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+bTwvbWk+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDIyMjA7PC9taT48bWk+UTwvbWk+PG1vPj08L21vPjxtc3VwPjxtbj4xNjU8L21uPjxtbz4mI3gyMjE4OzwvbW8+PC9tc3VwPjwvbWF0aD63PXsuAAAAAElFTkSuQmCC)
Use the Law of Detachment to make a valid conclusion in the true situation.
If the measure of an angle is less than 90°, then it is an acute angle.
![m straight angle Q equals 165 to the power of ring operator](data:image/png;base64,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)
Find JK
![](data:image/png;base64,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)
Find JK
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)
A girl bought two packs of gum from the store. Later she thought she would need some more gum and went back to the store to buy three more packs of gum. If she paid a total of $5.70 for gum, how much was each pack of gum?
A girl bought two packs of gum from the store. Later she thought she would need some more gum and went back to the store to buy three more packs of gum. If she paid a total of $5.70 for gum, how much was each pack of gum?
Use the Law of Detachment to make a valid conclusion in the true situation.
If angles form a linear pair, then they are supplementary.
∠𝐴 𝑎𝑛𝑑 ∠𝐵 form a linear pair.
Use the Law of Detachment to make a valid conclusion in the true situation.
If angles form a linear pair, then they are supplementary.
∠𝐴 𝑎𝑛𝑑 ∠𝐵 form a linear pair.
A man buys four books from the store and a Preferred Reader discount card for $20. Later that day, he goes back and buys five more books. He also got a $5 discount using his new card. If he spent a total of $87 at the bookstore, how much did each book cost assuming every book cost the same amount?
A man buys four books from the store and a Preferred Reader discount card for $20. Later that day, he goes back and buys five more books. He also got a $5 discount using his new card. If he spent a total of $87 at the bookstore, how much did each book cost assuming every book cost the same amount?
Show the conjecture is false by finding a counterexample. If the product of two numbers is even, then the two numbers must be even.
Show the conjecture is false by finding a counterexample. If the product of two numbers is even, then the two numbers must be even.
Dimple Bought a Calculator and binder that were both 15% off the original price. The
original price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was the
original price of the calculator?
The x + 2 = 6 x+2=6x, plus, 2, equals 6 contains a variable. We call this type of equation with a variable an algebraic equation. Finding the variable value that will result in a true equation is typically our aim when solving an algebraic equation.
¶Variables or constants are the two types of measurable quantities. A variable is a quantity with a varying value, and the constant value is nothing but a constant.
¶Steps to writing Variable Equation
1) Identify the variables that represent the unknowns.
2) Convert the issue into variable expressions in algebra.
3) Determine the variables' values to solve the equations for their true values.
Dimple Bought a Calculator and binder that were both 15% off the original price. The
original price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was the
original price of the calculator?
The x + 2 = 6 x+2=6x, plus, 2, equals 6 contains a variable. We call this type of equation with a variable an algebraic equation. Finding the variable value that will result in a true equation is typically our aim when solving an algebraic equation.
¶Variables or constants are the two types of measurable quantities. A variable is a quantity with a varying value, and the constant value is nothing but a constant.
¶Steps to writing Variable Equation
1) Identify the variables that represent the unknowns.
2) Convert the issue into variable expressions in algebra.
3) Determine the variables' values to solve the equations for their true values.