Applied Math: Example Applied Math Problems

Level 3 Sample Question

Question: At the grocery store, Steve bought $33.81 of food. He paid in cash, handing the cashier $40. How much change should he receive?

A. $3.81 B. $6.19 C. $16.19 D. $13.81 E. $40.00

This is a level 3 problem because it is straightforward in what it asks and it presents only the information you need to answer the question.
 

Explanation: To figure out how much change Steve should receive you must subtract the cost of the food from the amount of money he handed the cashier. The following demonstrates that
the correct answer is choice B:
$40.00
$33.81
$ 6.19

Level 5 Sample Question
Question: A warehouse club member purchased flooring for $27.18 per box. The warehouse club reported that the member had saved over $250 by purchasing the flooring from them rather than from the local retailer who was selling it for $61.04 per box. What is the minimum number of boxes of flooring the member would have had to purchase to save over $250?

A. 7 B. 8 C. 27 D. 33 E. 34

This is a level 5 problem because the way in which the information is presented is more complicated and because it requires higher reasoning and more varied operations to solve.
Explanation: The amount saved per box of flooring is .

To find the number of boxes of flooring the member would have to purchase to save $250, divide $250 by the amount saved per box, or $33.86, and you get  rounded to the nearest hundredth. Although this number rounds to 7 when you round to the nearest whole number, if the member purchased 7 boxes of flooring, the total savings would be , which is not over $250.

The member would have to purchase at least 8 boxes of flooring to save over $250. , which clearly meets the requirements of the given conditions. 

Answer choice B is correct.

Level 7 Sample Question
Question: A manufacturer uses an aluminum can 4 inches in diameter and 8 inches tall to sell soup. The manufacturer wants to switch to a cylindrical glass jar with a base only 3 inches in diameter. Which of the following best represents the required height of the glass jar, if the jar is to hold exactly the same amount of soup?
A.       inches
B.      inches
C.       inches
D.      inches
E.       inches
This is a level 7 question because it required you to use the volume formula for a cylinder to calculate multiple volumes and fill in missing information.
Explanation: The volume of a cylinder can be determined by using the formula , where r is the radius of the cylinder and h is the height. In both cylinders in the problem, the diameter is given rather than the radius, so it must be divided by 2.

The volume of the aluminum can is equal to , or  inches. In order to find the necessary height of the glass jar, the radius of 1.5 inches and prior volume of the aluminum can need to be substituted into the volume formula as follows: .

Simplifying this gives us . Rearranging to solve for h gives us .

Dividing this out, the two pi’s cancel and h is approximately 14.22 inches. The height of  inches given by answer choice E is the choice that best represents the required height.