Question
An animal shelter categorizes donors based on their total yearly donation, as shown in the table.
Keenan donates the same amount each month. Write and solve a compound inequality for the monthly donation that will put him in the gold category.
Hint:
If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
The correct answer is: Hence, Keenan should donate $41.67 to $83.33 monthly to put him in the gold category but not $83.33
To become a gold category donor member, one must donate between $500 to $1000 in one year
A year consists of 12 months. Let’s say that the donation made by Keenan in one month is x
So, $500 ≤ 12x < $1000
Solving the inequality
500 ≤ 12x < 1000
Dividing 12 on all sides
41.67 ≤ x < 83.33
Final Answer:
Hence, Keenan should donate $41.67 to $83.33 monthly to put him in the gold category but not $83.33
Dividing 12 on all sides
Final Answer:
Hence, Keenan should donate $41.67 to $83.33 monthly to put him in the gold category but not $83.33
A compound inequality is a solution that involves or includes the solutions to one inequality and the solutions to the other inequality, x<a or x>b. The compound inequality solution includes only solutions to both inequalities where they coincide. x<a and x>b=>a<x<b. It comprises two inequalities linked together by the words "and" or "or." Compound inequalities are inequalities that have two or more parts. These parts can be either "or" or "and."
For example, if an inequality states that "x is greater than '5' but less than 10," then x could be any number between 5 and 10. To solve a compound inequality, you must find all the variable values that make the compound inequality true. We solve each inequality individually and then compare the two solutions.
Related Questions to study
What is the synonym of know
What is the synonym of know
What is the solution of 0.2x-4-2x < -0.4 and 3x+2.7 < 3
What is the solution of 0.2x-4-2x < -0.4 and 3x+2.7 < 3
Fill in the blank with antecedent pronoun Neither Rachel nor Alice is responsible for ______failure.
Fill in the blank with antecedent pronoun Neither Rachel nor Alice is responsible for ______failure.
To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
What is the synonym of recommendation
What is the synonym of recommendation
Identify the kind of underlined verb in the sentence . Jacob and Jack are planning to submit mount Everest.
Identify the kind of underlined verb in the sentence . Jacob and Jack are planning to submit mount Everest.
Find the Monitor diagonal length?
Find the Monitor diagonal length?
Identify the kind of sentence Orange did not go to school as it was raining.
Identify the kind of sentence Orange did not go to school as it was raining.
Recognize the part of speech of the underlined word You should not do so
Recognize the part of speech of the underlined word You should not do so
What is the synonym of historical?
What is the synonym of historical?
Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
A peanut company ships its product in a carton that weighs 20 oz when empty. Twenty bags of peanuts are shipped in each carton. The acceptable weight for one bag of peanuts is between 30.5 oz and 33.5 oz, inclusive. If a carton weighs too much or too little, it is opened for inspection. Write and solve a compound inequality to determine x, the weight of cartons that are opened for inspection
The compound inequality statement for the weight of inspected cartons is 630 > X > 690. Here, It can also explain like this:
¶Empty carton weight = 20 oz.
Acceptable weight range per bag of peanuts:
The lower limit is 30.5 oz.
Maximum weight = 33.5 oz
20 bags = 20 peanut bags per carton
Therefore,
The following is the lower limit for carton weight after filling:
630 oz = weight of empty carton + (20 * weight per bag) 20 + (20 * 30.5)
The maximum weight of a carton after it has been filled will be:
Empty carton weight + (20 * weight per bag) 20 + (20 * 33.5) = 690 oz
As a result, the compound inequality for the inspected cartons is: 630 > X > 690.
A peanut company ships its product in a carton that weighs 20 oz when empty. Twenty bags of peanuts are shipped in each carton. The acceptable weight for one bag of peanuts is between 30.5 oz and 33.5 oz, inclusive. If a carton weighs too much or too little, it is opened for inspection. Write and solve a compound inequality to determine x, the weight of cartons that are opened for inspection
The compound inequality statement for the weight of inspected cartons is 630 > X > 690. Here, It can also explain like this:
¶Empty carton weight = 20 oz.
Acceptable weight range per bag of peanuts:
The lower limit is 30.5 oz.
Maximum weight = 33.5 oz
20 bags = 20 peanut bags per carton
Therefore,
The following is the lower limit for carton weight after filling:
630 oz = weight of empty carton + (20 * weight per bag) 20 + (20 * 30.5)
The maximum weight of a carton after it has been filled will be:
Empty carton weight + (20 * weight per bag) 20 + (20 * 33.5) = 690 oz
As a result, the compound inequality for the inspected cartons is: 630 > X > 690.
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
