How many of each item did she buy?

Question

You spend $63 on books and movies. Yiu pay $12 per book and $15 per movie. You buy 3 more books than movies.Jow many of each item did you buy?

Answer 1

b= the number of books

m=the number of movies

63=12b+15m This means that the total amount spent equals (the price of each book times the number of books bought) added to (the price of each movie times the number of movies bought.)

Since there are three more books than movies, we know that b=m+3 because if we buy three more movies, we would have the same number of movies as books. Because b=m+3, we can substitute m+3 for b in our original equation and we get 63=12(m+3)+15m.

We distribute the 12 by multiplying and we get 63=12m+36+15m.

We add the Ms and we get 63=27m+36.

We subtract 36 from both sides of the equation and we get 27=27m,

We divide both sides by 27 to get m by itself and we see that 1=m, or m=1.

If m=1, then b=4 because we were told that there were three more books bought than movies bought.

Answer 2

B - M = 3

12B+ 15M = 63

Solve the system of equations!

Multiply each term in the first system by 12, leaving you with the following equations:

12B - 12M = 36

12B + 15M = 63

Subtract one from the other:

12B + 15M = 63

-(12B - 12M = 36

-------------------------

0 + 27M = 27

27M = 27

M = 1

B - M = 3 (from the original equations)

B - 1 = 3

B = 4

You bought 4 books and 1 movie.