Question

a bookstore took in$ 167 on the sale of 5 copies of a new cookbook and 3 copies of a new novel the next day it took in $ 89 on the sale of 3 copies of the cookbook and 1 copy of the novel.what was the price of each book?

Answer 1

I am going to use C to represent cookbook and N to represent N. I find that easier to remember which is which.

Day 1: 5C + 3N = 167

Day 2: 3C + 1N = 89

We need to solve one of these equation for either the C or N. I always choose the easiest one! Day 2 looks like the one.

3C + 1N = 89 (I am doing to solve for N because we won't have a fraction)

1N=89-3C

N=89-3C

Now we take this solution for N and put it into our first equation.

5C + 3(89-3C) = 167 (We need to distribute)

5C + 267 - 9C = 167 (Use subtraction to move C values to the right and numbers to the left)

267-167 = 9C-5C

100 = 4C

25 = C $25 for the Cookbooks.

Now, we have to go back and solve for N by putting $25 in for C in the second equation.

N=89-3(25)

N=89-75

N=14 dollars for each novel.

Check by putting both back into the first equation:

5C + 3N = 167

5(25) + 3(14) = 167. It checks out!