Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Tom wants to make scrapbooks with old family photos. An online scrapbooking company charges $\$39$ for a basic book and $\$4$ per page. Meanwhile, a family friend is willing to make a scrapbook for $\$48$ plus $\$1$ 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

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

\$39

for a basic book and

\$4

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

\$48

plus

\$1

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. $\newline$ Now, we can write the equations for the cost of the scrapbook from the online company and the family friend. $\newline$ For the online scrapbooking company: $\newline$ $y = 4x + 39$
Write Equations: For the family friend: $y = x + 48$
Set Equations Equal: We want to find the number of pages $x$ for which the cost $y$ would be the same from both the online company and the family friend. So we set the two equations equal to each other to find the value of $x$ : $4x + 39 = x + 48$
Solve for x: Now we solve for x by subtracting $x$ from both sides of the equation: $\newline$ $4x - x + 39 = x - x + 48$ $\newline$ $3x + 39 = 48$
Isolate x Term: Next, we subtract $39$ from both sides of the equation to isolate the term with $x$ : $\newline$ $3x + 39 - 39 = 48 - 39$ $\newline$ $3x = 9$
Solve for x: Now we divide both sides of the equation by $3$ to solve for x: $\newline$ $\frac{3x}{3} = \frac{9}{3}$ $\newline$ $x = 3$
Substitute $x$ : We have found that $x = 3$ , which means the scrapbook would have $3$ pages. Now we need to find the cost $y$ for $3$ pages. We can substitute $x = 3$ into either of the original equations. Let's use the first equation: $\newline$ $y = 4x + 39$ $\newline$ $y = 4(3) + 39$
Calculate Total Cost: Now we calculate the total cost: $\newline$ $y = 4 \times 3 + 39$ $\newline$ $y = 12 + 39$ $\newline$ $y = 51$