Two companies are competing with one another for a contract to provide work uniforms to a customer, which is a large global manufacturing business. Company A sells its uniforms for \$25 per uniform, and Company B's price is \$30 per uniform. Both companies sell their uniforms in lots of 5,000 each. The customer has considered ordering some uniforms from both companies, in order to test them out before committing to one company on an ongoing basis. The company wants to spend exactly \$1,000,000 on the test purchase.

In the table below, identify the number of uniforms that the customer should buy from Company A and from Company B so that the customer spends exactly \$1,000,000. Make only one selection in each column.
Company ACompany BNumber of Uniforms
5,000
10,000
15,000
25,000
30,000
40,000

Company ACompany BNumber of Uniforms
5,000
10,000
15,000
25,000
30,000
40,000

This problem, like other 2-part reasoning problems, asks you to find the one solution (out of many potential solutions) that is present in the table. We must first create an algebraic model for the situation at hand. We have shirts from Company A that cost \$25 each, and shirts from Company B that cost \$30 each, and that we want to spend exactly \$1,000,000. This gives us the following model:

25A + 30B = 1,000,000

We also know that each must be purchased in bundles of 5,000 shirts (that is, A and B must both be multiples of 5,000), but the answer choices already take this into account for us. By testing values from one column, you will find that the correct answer is A = 10,000, B = 25,000.

25(10,000) + 30B = 1,000,00
30B = 750,000
B = 25,000

Blindly testing values can be time-consuming, however, so it is often to your advantage to look for ways to simplify your search. For example, you could subtract 25A from the left-hand side, and divide all terms by 5 to rewrite the equation above as:

6B = 200,000 - 5A

Framing the equation in this manner should help you quickly eliminate some of the larger values from Column A, encouraging you to spend your time checking the smaller values instead - and finding the correct answer in the process.