A shipping company employee is in charge of packing cargo containers for shipment. He knows a certain cargo container can hold a maximum of 50 microwaves or a maximum of 15 refrigeratiors. Each microwave takes up 6 cubic feet of space, and each refrigerator takes up 20 cubic feet. The cargo container can hold a maximum of 300 cubic feet. The employee is trying to figure out how to pack a container containing both microwaves and refrigerators. Which of the following system of inequalities can the employee use to determine how many of each item (microwaves, m, and refrigeratios, r) he can pack into one cargo container ?

Options

A. `m le 6`
`r le 20`
`50m + 15r le 300`
B. `mle 50`
`r le 15`
`m + r le 300`
C. `m le 50`
`r le 15`
`6m+ 20r le 300`
D. `m le 50`
`r le 15`
`50m + 15r le 300`

Answer

C

Explanation

The clue "holds a maximu" means the container can hold exactly that much or less, so use the less than or equal to symbol ` (le)` throughout. The cargo container can hld a maximum of 50 microwaves, so the first inequality is ` m le 50.` Eliminate (A). The container can hold a maximum of 15 refrigerators, so the second inequality is `r le 15.` The third inequality deals with the size of each appliance. The cargo container can hold m microwaves multiplied. by the size of the microwave, whihc is 6 cubic feet, it can hold r refrigerators multiplies by the size of the refrigerator, which is 20 cubic feet, and it can hold maximum of 300 cubic feet total. Put these together to write the findal inequality: `6m +20r le 300, ` which is (C ).