Write a system of equations to describe the situation below, solve using elimination.
A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Yamamoto purchased 42 new hardcover books and 64 new paperback books, which cost a total of $698. He also purchased 42 new hardcover books and 58 new paperback books for the adult fiction section, spending a total of $668. What is the special price for each type of book?

Question

29-01-2020
Mathematics

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Write a system of equations to describe the situation below, solve using elimination.
A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Yamamoto purchased 42 new hardcover books and 64 new paperback books, which cost a total of $698. He also purchased 42 new hardcover books and 58 new paperback books for the adult fiction section, spending a total of $668. What is the special price for each type of book?

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ChiKesselman ChiKesselman · Answer 1 · 2020-01-29T07:01:42+01:00

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:

[tex]42x + 64y = 698[/tex]

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

We can write the equation as:

[tex]42x + 58y = 668[/tex]

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

We eliminate x by subtracting the two equations.

[tex]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[/tex]

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