Writing an Inequality for a Real-World Situation Online Quiz

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Q 1 - The width of a rectangle is 26 centimeters. The perimeter is at least 192 centimeters. Let the length of the rectangle be l. Write an inequality for this situation.

Answer : A

Explanation

Step 1:

Given w = 26 cm; Perimeter ≥ 192

Perimeter of the rectangle = 2(l + w);

Step 2:

Inequality representing the above real-world situation is 2(1 + 26) ≥ 192

Q 2 - Brenda rented a bike from Bruno's Bikes. They charged her $4 per hour, plus a $10 fee. Linda paid less than $30. Let h be the number of hours Linda rented the bike. Write an inequality for this situation.

Answer : C

Explanation

Step 1:

Given per hour rate = $4; fixed amount = $10

Amount paid = 4h + 10 < 30

Step 2:

Inequality representing the above real-world situation is (4h + 10) < 30

Q 3 - Shawna needs to buy some pencils and an eraser. She can spend no more than $9. The eraser costs $2 and the pencils cost $0.35 each. Let the number of pencils Shawna buys be p. Write an inequality for this situation.

Answer : D

Explanation

Step 1:

Given eraser cost = $2; pencil cost = $0.35

Amount paid = 0.35p + 2 ≤ 9

Step 2:

Inequality representing the above real-world situation is 0.35p + 2 ≤ 9

Q 4 - Phil is saving $10 each week. He earns an extra $12 by mowing his neighbor's lawn. How many weeks will he need to save to have at least $92? Let Phil work for m number of weeks to save the amount. Write an inequality for this situation.

Answer : B

Explanation

Step 1:

Given Savings/week = $10; extra income = $12

Amount saved = 10m + 12 ≥ 92

Step 2:

Inequality representing the above real-world situation is 10m + 12 ≥ 92

Q 5 - Mojo's Canoes rents canoes for $30 plus $40 per hour. You do not want to spend more than $190. For how many hours can you afford to rent the canoe? Let the number of hours you can rent the canoe be h. Write an inequality for this situation.

Answer : C

Explanation

Step 1:

Given Rent/hour = $40; fixed amount = $30;

Amount spent = 40h + 30 ≤ 190

Step 2:

Inequality representing the above real-world situation is 40h + 30 ≤ 190

Q 6 - Monica won 42 lollipops playing volleyball at the school fair. She gave one to every student in her math class. She has at least 7 lollipops left. Let the number of students in her class be s. Write an inequality for this situation.

Answer : A

Explanation

Step 1:

Given Lollipop/student = 1; lollipops left ≥ 7

Leftover lollipops = 42 − 1s ≥ 7

Step 2:

Inequality representing the above real-world situation is 42 − 1s ≥ 7

Q 7 - Mark spent less than $26 on a magazine and four composition books. The magazine cost $6. Let the cost of a composition book be z. Write an inequality for this situation.

Answer : B

Explanation

Step 1:

Given Magazine cost = $6; book cost = z;

Amount spent = 4z + 6 < 26

Step 2:

Inequality representing the above real-world situation is 4z + 6 < 26

Q 8 - More than 340 students went on a field trip. Eleven buses were filled and 10 more students traveled in a car. Let s represent the number of students in each bus. Write an inequality for this situation.

Answer : D

Explanation

Step 1:

Number of buses = 11; students in car = 10;

Total students = 11s + 10 > 340

Step 2:

Inequality representing the above real-world situation is 11s + 10 > 340

Q 9 - Nathan walks his dog more than 28 minutes every day. Let t represent the time in minutes that Nathan walks his dog. Write an inequality for this situation.

Answer : B

Explanation

Step 1:

Time Nathan walks his dog > 28 minutes

Step 2:

Inequality representing the above real-world situation is t > 28

Q 10 - For a field trip 25 students rode in cars and the rest filled seven buses. How many students were in each bus if no more than 305 students went on the trip? Let number of students in each bus be x. Write an inequality for this situation.

Answer : A

Explanation

Step 1:

Number of buses = 7; students in car = 25;

Total students = 7x + 25 ≤ 305

Step 2:

Inequality representing the above real-world situation is 7x + 25 ≤ 305

writing_an_inequality_for_real_world_situation.htm