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miguel spends $100 on books, five of which are hardcover and the remaining four are paperback. the prices at the bookstore are based on whether the book is hardcover or paperback. it charges $2 less for paperback books than for hardcover books. what is the price for hardcover books?

For this case we propose a system of equations:

a: Let the variable representing the cost of hardcover books

b: Let the variable representing the cost of paperback books

According to the statement data we have:

Substituting the second equation into the first we have:

Thus, the cost of hardcover books is $12

The cost of hardcover books is $12

Answers and Step-by-step explanations:

A. We have a total of 4 4/5 feet of rope, but we want lots of little 2/5 feet pieces of rope. In order to find how many we can get, we need to divide 4 4/5 by 2/5.

To do so, first convert 4 4/5 into an improper fraction, as that makes it easier: 4 4/5 = 24/5.

Now divide the two fractions. Remember that when you divide fractions, it is equivalent to multiplying by the reciprocal of the divisor:

(24/5) / (2/5) = (24/5) * (5/2) = 12 pieces

B. The quotient from Part A is 12, and its meaning is that there are 12 pieces of the 2/5 feet of rope that Tara can cut the original long rope into.

Hope this helps!