Question

A truckload of 10lb and 50lb bags of fertilizer weighs 9000 pounds. A second truck carries twice as many 10lb bags and half as many 50lb bags as the first truck. That load also weighs 9000 pounds. How many of each bag are on the first truck?

Answer 1

To solve this problem, set up a system of equations. The first truck carries 400 10lb bags and 100 50lb bags.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the number of 10lb bags and y represent the number of 50lb bags on the first truck. From the information given, we can set up the following equations:

x + y = ? (equation 1)

10x + 50y = 9000 (equation 2)

Next, we can set up equations for the second truck. Since it carries twice as many 10lb bags and half as many 50lb bags as the first truck, we have:

2x + (0.5)y = ? (equation 3)

10(2x) + 50(0.5)y = 9000 (equation 4)

Solving equations 1 and 2 simultaneously, we find that x = 400 and y = 100. Substituting these values into equations 3 and 4, we find that the second truck carries 800 10lb bags and 50 50lb bags. Therefore, the first truck carries 400 10lb bags and 100 50lb bags.