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On a website selling books, three paperback books and five hardcover books cost $80.10, and seven paperback books and four hardcover books cost $100.65. What is the total cost of one paperback and one hardcover book?

Respuesta :

To answer this kind of question, you need to insert the first equation into second equation or vice versa. The equation from the question should be:

1. 3 paperback books +  5 hardcover book = $80.10
2. 7 paperback books + 4 hardcover book= $100.65

It would be easier to convert the 1st equation into
5 hardcover book = $80.10- 3 paperback books
hardcover book= $16.02- 0.6 paperback books

Then insert it to 2nd equation:
7 paperback books + 4 ($16.02- 0.6 paperback books)= $100.65
7 paperback books + $64.08- 2.4 paperback books= $100.65
4.6 paperback books = $100.65-  $64.08= $36.57
paperback book= $7.95

Insert paperback book price to the first equation to find the hardcover book price
3 paperback books +  5 hardcover book = $80.10
3 ($7.95)+  5 hardcover book = $80.10
5 hardcover book = $80.10 - $23.85= $56.25
hardcover book = $11.25

Then one paperback and one hardcoverbook= $7.95 + $11.25= $19.20 

Let us represent

Paperback books = p

Hardcover books = h

Three paperback books and five hardcover books cost $80.10

3p + 5h = 80.10..........Equation 1

Seven paperback books and four hardcover books cost $100.65

7p + 4h = 100.65.......Equation 2

Step 1

We have to find the cost of each paperback and hardcover book. We do this using the Elimination Method.

3p + 5h = 80.10..........Equation 1

7p + 4h = 100.65.......Equation 2

Multiply Equation 1 by 4 and Equation 2 by 5 to eliminate h

12p + 20h = 320.4........Equation 3

35p + 20h = 503.25.......Equation 4

We subtract Equation 3 from Equation 4

23p = 182.85

We divide both sides by 23

23p/23 = 182.85/23

p = 7.95

The cost of one paperback book is $7.95

We solve for h, the cost of one hardback book by substituting 7.95 in Equation 1

3p + 5h = 80.10..........Equation 1

3(7.95) + 5h = 80.10

23.85 + 5h = 80.10

5h = 80.10 - 23.85

5h = 56.25

We divide both sides by 5

5h/5 = 56.25/5

h = 11.25

The cost of one hardback book is $11.25

Step 2

The cost of one paperback book is $7.95

The cost of one hardback book is $11.25

The total cost of one paperback and one hardcover book is

$7.95 + $11.25 = $19.20

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https://brainly.com/question/20160304