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14. Steve has a $50 gift certificate from the local bookstore. He was planning to spend the entire amount by purchasing 3 hard-cover books and 4 paperback books. However, he bought only 2 hard-cover books and 3 paperback books, and he still has $15.50 left on the gift certificate. Find the cost of a hard-cover book and the cost of a paperback book.

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Answer:Let x be the cost of a hard-cover book and y be the cost of a paperback book.

We know that Steve spent 2 hard-cover books and 3 paperback books. So we can write the equation as:

2x + 3y = 50 - 15.5

2x + 3y = 34.5

We also know that he was planning to buy 3 hard-cover books and 4 paperbacks, so we can write another equation as:

3x + 4y = 50

Now we have a system of two equations with two unknowns:

2x + 3y = 34.5

3x + 4y = 50

We can use the first equation to eliminate one variable by multiplying both sides by 2 and then subtracting 3y:

4x + 6y = 69

3x + 4y = 50

x = 19.5

Now we can substitute this value of x into the second equation and find the value of y:

3(19.5) + 4y = 50

58.5 + 4y = 50

4y = -8.5

y = -2.125

Therefore, the cost of a hard-cover book is $19.5 and the cost of a paperback book is $-2.125.

Note that the cost of a paperback book is a negative value which is not possible in this case. It means that the given information does not have a solution.

Explanation:

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