Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Derek wants to make scrapbooks with old family photos. An online scrapbooking company charges $\$10$ for a basic book and $\$4$ per page. Meanwhile, a family friend is willing to make a scrapbook for $\$43$ 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

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

\$10

for a basic book and

\$4

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

\$43

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 $x$ represent the number of pages in the scrapbook. $\newline$ Let $y$ represent the total cost of the scrapbook.
Write Equations: Write the equations based on the given information. $\newline$ For the online scrapbooking company: $y = 10 + 4x$ (since the basic book is $\$10$ and each page is $\$4$ ). $\newline$ For the family friend: $y = 43 + x$ (since the basic book is $\$43$ and each page is $\$1$ ).
Set up System: Set up the system of equations. $\newline$ We have two equations: $\newline$ $1$ ) $y = 10 + 4x$ $\newline$ $2$ ) $y = 43 + x$
Solve by Substitution: Solve the system using substitution. $\newline$ Since both equations equal $y$ , we can set them equal to each other to find the value of $x$ : $\newline$ $10 + 4x = 43 + x$
Solve for x: Solve for x. $\newline$ Subtract $x$ from both sides: $\newline$ $10 + 4x - x = 43 + x - x$ $\newline$ $10 + 3x = 43$
Isolate Variable Term: Subtract $10$ from both sides to isolate the variable term. $\newline$ $3x = 43 - 10$ $\newline$ $3x = 33$
Calculate $x$ : Divide both sides by $3$ to solve for $x$ .
$x = \frac{33}{3}$
$x = 11$
Substitute $x$ : Substitute $x$ back into one of the original equations to find $y$ . Using the first equation: $y = 10 + 4x$ $y = 10 + 4(11)$
Calculate $y$ : Calculate the value of $y$ . $y = 10 + 44$ $y = 54$
Final Answer: Write the final answer. $\newline$ The scrapbook would cost $\$54$ if it had $11$ pages.