algebra 2 problem

Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 96 kilograms. A delivery of 8 large boxes and 3 small boxes has a total weight of 163 kilograms. How much does each type of box weigh?

Answer 1

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 96 kilograms. A delivery of 8 large boxes and 3 small boxes has a total weight of 163 kilograms. How much does each type of box weigh?

1. set up equations for each of the two scenarios:
2. 2(L) + 5(S) = 96
3. 8(L) + 3(S) = 163
4. Now use one of the equations to solve for 1 of the variables, and plug that equation into the second equation (so the second equation will have all the same variable). Then you can solve for that variable:
5. 2L = 96 - 5S: L = (96-5S)/2 use this for the (L) in the second equation
6. 8((96-5S)/2) + 3(S) = 163 now solve for S
7. S = 13 kilograms use this answer to plug into either equation and solve for (L)
8. L = 15.5 kilograms

Does the process make sense to you? What questions do you have with the process?