Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Vince wants to make scrapbooks with old family photos. An online scrapbooking company charges $\$19$ for a basic book and $\$4$ per page. Meanwhile, a family friend is willing to make a scrapbook for $\$37$ plus $\$3$ per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be? $\newline$ The scrapbook would cost $\$$ _ if it had _ pages.

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Solve a system of equations using substitution: word problems

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Vince wants to make scrapbooks with old family photos. An online scrapbooking company charges

\$19

for a basic book and

\$4

per page. Meanwhile, a family friend is willing to make a scrapbook for

\$37

plus

\$3

per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be?

\newline

The scrapbook would cost

\$

_____ if it had _____ pages.

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of pages in the scrapbook. $\newline$ Let $y$ be the total cost of the scrapbook. $\newline$ The online scrapbooking company charges $\$19$ for a basic book and $\$4$ per page. So the equation for the cost of the scrapbook from the online company is: $\newline$ $y = 4x + 19$
Online Company Cost Equation: The family friend charges $\$37$ for a basic book and $\$3$ per page. So the equation for the cost of the scrapbook from the family friend is: $\newline$ $y = 3x + 37$
Family Friend Cost Equation: We want to find the number of pages for which the price from both the online company and the family friend would be equal. This means we need to set the two equations equal to each other and solve for $x$ : $4x + 19 = 3x + 37$
Set Equations Equal: Now we solve for $x$ by subtracting $3x$ from both sides of the equation: $\newline$ $4x + 19 - 3x = 3x + 37 - 3x$ $\newline$ $x + 19 = 37$
Solve for x: Next, we subtract $19$ from both sides to solve for $x$ : $\newline$ $x + 19 - 19 = 37 - 19$ $\newline$ $x = 18$
Substitute $x$ into Equation: Now that we have the value of $x$ , we can substitute it back into either of the original equations to find the total cost $y$ . We'll use the first equation: $\newline$ $y = 4x + 19$ $\newline$ $y = 4(18) + 19$
Calculate Total Cost: Perform the multiplication and addition to find $y$ : $y = 72 + 19$ $y = 91$
Final Answer: We have found that the scrapbook would cost $\$91$ if it had $18$ pages. This answers the question prompt.