A printer charges $8.00 to set up each job and an additional $6.00 per box of 20 invitations printed. Write an inequality to determine the greatest number of boxes of invitations that could be printed for under $100.

A. 100 > 8 − 6x
Incorrect. The rate of change is increasing, so the x-term will not be subtracted from the initial set up charge.

B. 100 > 8 + 6x
Correct!

C. 100 ≥ 8 + 6x
Incorrect. If the cost is exactly $100, will it be under $100?

D. 100 < 8 + 6x
Incorrect. The expression 8 + 6x represents the cost of having the invitations printed. Will this quantity be greater than $100 or less than $100?

The Nguyen family is traveling to visit friends in Louisiana. The total trip is 175 miles. The family has already driven x miles of the trip to Louisiana. If they drive below 65 miles per hour for the remainder of the trip, which inequality best represents the amount of time in hours, t, that it will take them to complete the remainder of the drive? Select A, B, C or D.

The weight limit for a boat used by the Highland Lakes College Rowing Team is 2,140 pounds. The average weight of an oarsman on the team is 225 pounds. Write an inequality that can be used to determine the number of oarsmen, n, that can be on a boat that weighs b, pounds without exceeding the weight limit.

A. 2,140 < 225n + b
Incorrect. The expression 225n + b represents the combined weight of the oarsmen and the boat. Which is greater: this quantity or 2,140 pounds?

B. 2,140 ≤ 225n + b
Incorrect. The expression 225n + b represents the combined weight of the oarsmen and the boat. Which is greater: this quantity or 2,140 pounds?

C. 2,140 > 225n + b
Incorrect. If the combined weight of the oarsmen and the boat is exactly equal to 2,140 pounds, will it exceed the weight limit?

D. 2,140 ≥ 225n + b
Correct!

Mrs. Landis raises dogs and shows them at dog shows. She has a van that she uses to transport dogs to the dog show. A miniature poodle has an average weight of 14.8 pounds and a beagle has an average weight of 23 1 2 pounds. Mrs. Landis can transport no more than 850 pounds in her van. Which inequality best describes the number of poodles, p, and the number of beagles, b, that Mrs. Landis can transport in her van?

A. 14.8b + 23 1 2 p ≤ 850
Incorrect. 14.8 pounds represents the average weight of a poodle, so this number needs to go with p, the variable that represents the number of poodles. Likewise, 23 1 2 represents the average weight of a beagle, so this number needs to go with b, the variable that represents the number of beagles.

B. 14.8b + 23 1 2 p < 850
Incorrect. 14.8 pounds represents the average weight of a poodle, so this number needs to go with p, the variable that represents the number of poodles. Likewise, 23 1 2 represents the average weight of a beagle, so this number needs to go with b, the variable that represents the number of beagles.

C. 14.8p + 23 1 2  b ≤ 850
Correct!

D. 14.8p + 23 1 2  b < 850
Incorrect. If the combined weight of the poodles and the beagles is no more than 850 pounds, then 850 pounds is a possible combination, so we need to include "or equal to."

Which of the following situations could not be represented with the inequality,
410 ≥ 145.9 + 21.4x?

A. A box weighs 145.9 grams, and a package of crackers weighs 21.4 grams. What is the greatest number of packages of crackers that be packed in the box without exceeding a total weight of 410 grams?
Incorrect. This situation matches the inequality. Because 410 is greater than or equal to the expression, the expression must be less than or equal to 410.

B. A vehicle has a fuel efficiency of 21.4 miles per gallon, and the fuel tank holds enough fuel for 410 miles of driving. If the vehicle began with a full tank of fuel and has been driven for 145.9 miles, how many more miles can the vehicle be driven without running out of fuel?
Incorrect. This situation matches the inequality. The number of miles that the vehicle is driven cannot exceed 410 miles, so 410 must be greater than the expression used to calculate the number of miles driven on one tank of fuel.

C. Mari has $145.90 in savings and wants to earn enough money to purchase a mini tablet computer that costs $410. She can save $21.40 from each yard that she rakes. How many yards must Mari rake before her savings will exceed the amount of money necessary to purchase the mini tablet computer?
Correct! In this situation, $410 must be less than the expression showing the amount of money that Mari has saved. The symbol relating 410 with 145.9 + 21.4x shows that $410 would be greater than this amount, and the amount of money that Mari has saved would not exceed the cost of the mini tablet computer.

D. Ms. Johanssen received a grant for $410 to purchase equipment for her math class. She will purchase a projector that costs $145.90, and wants to use the remaining money to purchase calculators that cost $21.40 each. How many calculators can Ms. Johanssen purchase?
Incorrect. This situation matches the inequality. The amount of money spent cannot exceed $410, so $410 must be greater than the combined cost of the projector and x number of calculators.