Question

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write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
eliana wants to make scrapbooks with old family photos. an online scrapbooking company charges $9 for a basic book and $4 per page. meanwhile, a family friend is willing to make a scrapbook for $36 plus $1 per page. for a certain number of pages, the price would be equal.
how many pages would that be? how much would that cost?
if the scrapbook had pages, it would cost $
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Explanation:

Step1: Define variables

Let \(x\) be the number of pages.

Step2: Write equations

For Eliana's scrapbooks: \(y = 9+4x\) (where \(y\) is the total cost, \(9\) is the cost of the basic book and \(4x\) is the cost for \(x\) pages at \(4\) dollars per page).
For the online company: \(y = 36 + 1x\) (where \(36\) is the base cost and \(1x\) is the cost for \(x\) pages at \(1\) dollar per page).

Step3: Set equations equal

Set \(9 + 4x=36+x\).
Subtract \(x\) from both sides: \(9+4x - x=36+x - x\), so \(9 + 3x=36\).
Subtract \(9\) from both sides: \(3x=36 - 9\), so \(3x = 27\).
Divide both sides by \(3\): \(x=\frac{27}{3}=9\).

Step4: Find the cost

Substitute \(x = 9\) into either equation. Using \(y = 36+x\), we get \(y=36 + 9=45\).

Answer:

\(9\) pages, it would cost \(\$45\).