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

Martina wants to make scrapbooks with old family photos. An online scrapbooking company charges $41 for a basic book and $3 per page. Meanwhile, a family friend is willing to make a scrapbook for $45 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?


The scrapbook would cost $
 if it had 
 pages.


### Step 1: Define the variables
Let:
- $ x $ = number of pages in the scrapbook.
- $ y $ = total cost of the scrapbook.

### Step 2: Write the system of equations
The cost for the online scrapbooking company is:
\[
y = 41 + 3x
\]
The cost for the family friend is:
\[
y = 45 + 1x
\]

We want to find the number of pages ($x$) where the costs are equal ($y$).

### Step 3: Solve the system using substitution
Set the two equations equal to each other since the costs ($y$) are the same:
\[
41 + 3x = 45 + 1x
\]

Simplify the equation:
\[
3x - 1x = 45 - 41
\]
\[
2x = 4
\]
\[
x = 2
\]

Substitute $x = 2$ into one of the original equations to find $y$:
\[
y = 41 + 3(2)
\]
\[
y = 41 + 6
\]
\[
y = 47
\]

### Step 4: Write the final answer
The scrapbook would cost **\$47** if it had **2 pages**.

---

### Do you want further details or have any questions?

Here are **5 related questions** to expand your understanding:
1. How would the solution change if the family friend charged a flat fee of \$50 instead of \$45?
2. What is the cost difference for 10 pages between the two options?
3. How can the system of equations be solved using graphing instead of substitution?
4. What would be the break-even point if the per-page price for the online company increased to \$4?
5. Can you write a general formula to determine the break-even point for any flat fee and per-page price?

**Tip:** When solving systems of equations, substitution is most efficient when one variable is already isolated in at least one equation.

Martina wants to make scrapbooks with old family photos. An online scrapbooking company charges $41 for a basic book and $3 per page. Meanwhile, a family friend is willing to make a scrapbook for $45 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? The scrapbook would cost $ if it had  pages.

Learn how to solve a system of equations to determine the break-even point for two scrapbooking pricing options. The problem involves linear equations and substitution to find when both options cost the same. Suitable for students in Grades 7-9.

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