Question

Write a system of equations to describe the situation below, solve using elimination.

Answer 1

Answer:

The cost of hardbook is $9 and cost of paperback is $5.

Step-by-step explanation:

Let x be the price for hardback book and y be the price for paperback book.

Mr. Yamamoto purchased 42 new hardcover books and 64 new paperback books, which cost a total of $698.

We can write the equation as:

$42x + 64y = 698$

He also purchased 42 new hardcover books and 58 new paperback books, which cost a total of $668.

We can write the equation as:

$42x + 58y = 668$

We have to use the elimination method to solve the two equations.

We eliminate x by subtracting the two equations.

$42x + 64y-(42x + 58y) = 698 - 668\\\Rightarrow 6y = 30\\\Rightarrow y = 5\\42x + 64(5) = 698\\\\\Rightarrow x = \displaystyle\frac{698 - 64(5)}{42}\\\\\Rightarrow x = 9$

Thus, the cost of hardbook is $9 and cost of paperback is $5.