Question

1.

A train car can hold 1500 pounds of cargo that occupies 138 cubic feet of space. A computer
desk weighs 50 pounds and occupies a space of 4 cubic feet. A single drawer file cabinet weighs
30 pounds and occupies a space of 3 cubic feet. Which system of equations can be used to find
the total number of computer desks, d, and single drawer file cabinets, c, that can be carried in
the train car?
a. 4d + 3c = 138
50d + 30c = 1500
C. 50d + 30c = 138
30d + 3c = 138
b. 50d + 30c = 1500
50+ 4d = 1500
d. 4d + 3c = 138
30 + 3c = 1500

Answer 1

A

Explanation:

Let d be the total number of computer desks and c be the total number eof single drawer file cabinets.

1. A computer desk weighs 50 pounds, then d computer desks weigh 50d pounds. A single drawer file cabinet weighs 30 pounds, then c cabinets weigh 30c pounds. In total, a train car can hold 1500 pounds of cargo, so

50d+30c=1500

2. A computer desk occupies a space of 4 cubic feet, then d computer desks occupy 4d cubic feet. A single drawer file cabinet occupies a space of 3 cubic feet, then c cabinets occupy 3c cubic feet. In total, a train car can hold 138 cubic feet of space, so

4d+3c=138.

Thus, we get a system of two equations:

`\left \{ {{50d+30c=1500} \atop {4d+3c=138}} \right.`