John paid 34$ for two algebra and three geometry books. He paid $36 for three algebra and two geometry books. What is the cost of each book?

Answer 1

Hi Markaylon,

Here are the following steps you should follow to solve this problem. Answers below, but I encourage you to try this on your own first.

1. Write an equation that represents paying $34 for two algebra and three geometry books.
2. Write an equation that represents paying $36 for three algebra and two geometry books.
3. Find the LCM (Least Common Multiple) for the number of algebra books (2 and 3).
4. Multiply each equation by the number that would result in the LCM number of algebra books.
5. Subtract the equations from one another.
6. Solve the new equation to find out how much a geometry book costs.
7. Plug that cost into either original equation to find out how much an algebra book costs.

Note: Steps 3-7 is the standard method to solving a system of linear equations.

ANSWER:

1. 2a + 3g = $34 (where a = cost of 1 algebra book and g = cost of 1 geometry book)
2. 3a + 2g = $36
3. LCM of (2,3) = 6
4. 3*(2a + 3g = $34) = 6a + 9g = $102; 2*(3a + 2g = $36) = 6a + 4g = $72
5. (6a + 9g = $102) - (6a + 4g = $72) = (5g = $30)
6. 5g = $30 --> g = $6
7. 2a + 3($6) = $34 --> 2a = $16 --> a = $8