what were the cost of a bush and a tree?

Question

a landscaping company placed two orders with a nursery. the first order was for 13 bushes and 4 trees, and totaled $487. the second order was for 6 bushes and 2 trees, and totaled $232. the bills do not list the per-item price. what were the costs of one bush and of one tree?

Answer 1

I could try to add the bushes and trees, to get 19 bushes and 6 trees, but this wouldn't get me anywhere, because I don't have subtotals for the bushes and trees. So I'll pick variables ("b" for the number of bushes and "t" for the number of trees) and set up a system of equations:

first order: 13b + 4t = 487
second order: 6b + 2t = 232

Multiplying the second row by –2, I get:

13b + 4t = 487
–12b – 4t = –464
This says that b = 23. Back-solving, I get that t = 47. Of course, the exercise didn't ask for the values of the two variables. Translating back into English, the solution is:

 each bush is $23 and each tree is $47