Regina's teacher recently gave her a homework assignment on solving equations. Since she has been thinking about saving for a new cell phone, she decided to use the assignment as an opportunity to model a savings plan.
She created this equation to model the situation. In it, [tex]$y$[/tex] represents the total amount saved for the new cell phone, 74 is the amount of money she has now, 40 is the amount of money she saves each month for the phone, and [tex]$x$[/tex] represents the number of months since she started saving:
[tex]\[
74 + 40x = y
\][/tex]
She then solved the equation to determine how many months she'd need to save to have enough to purchase the new cell phone. Review her work and select the error.
[tex]\[
\begin{array}{|c|c|c|}
\hline
Justification & Steps & Work \\
\hline
\begin{tabular}{l}
1: Given \\
2: Subtraction Property of Equality \\
3: Simplification \\
4: Division Property of Equality \\
5: Simplification \\
6: Substitution, $y = 834$ \\
7: Simplification
\end{tabular}
&
\begin{tabular}{l}
Step 1: \\
Step 2: \\
Step 3: \\
Step 4: \\
Step 5: \\
Step 6: \\
Step 7:
\end{tabular}
&
\begin{tabular}{l}
\begin{aligned}
74 + 40x & = y \\
74 + 40x - 74 & = y - 74 \\
40x & = y - 74 \\
\frac{40x}{40} & = \frac{y - 74}{40} \\
x & = \frac{y - 74}{40} \\
x & = \frac{834 - 74}{40} \\
x & = 19
\end{aligned}
\end{tabular} \\
\hline
\end{array}
\][/tex]