Question

Luis spent $745.10 on 13 new file cabinet for his office. Small file cabinets cost $43.50 and large file cabinets cost $65.95. Write and solve a system of equations to find the number of smal cabinets and large cabinets he purchased.

Answer 1

Answer: he purchased 5 small file cabinets and 8 large file cabinets.

Step-by-step explanation:

Let x represent the number of small file cabinets that he purchased.

Let y represent the number of large file cabinets that he purchased.

Luis bought 13 new small and large file cabinets. This means that

x + y = 13

Small file cabinets cost $43.50 and large file cabinets cost $65.95. He spent a total of $745.10. This means that

43.5x + 65.95y = 745.1 - - - - - - - -1

Substituting x = 13 - y into equation 1, it becomes

43.5(13 - y) + 65.95y = 745.1

565.5 - 43.5y + 65.95y = 745.1

- 43.5y + 65.95y = 745.1 - 565.5

22.45y = 179.6

y = 179.6/22.45

y = 8

x = 13 - y = 13 - 8

x = 5