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Jerome's teacher gave him a homework assignment on solving equations. Since he's been thinking about saving for a used car, he decided to use the assignment as an opportunity to model a savings plan.

He already has [tex]$\$[/tex] 500[tex]$, and he plans to save $[/tex]\[tex]$ 375$[/tex] every month. To model the situation, he created this equation, where [tex]$y$[/tex] represents the total amount saved for the car and [tex]$x$[/tex] represents the number of months since he started saving:
[tex]\[ 500 + 375x = y \][/tex]

He then solved the equation to determine how many months he would need to save to have enough to purchase the car. Review his work, and select the error.

\begin{tabular}{|l|lr|}
\hline
\multicolumn{1}{|c|}{Justification} & & \\
\hline
1: Given & Step 1: & [tex]$500 + 375x = y$[/tex] \\
2: Addition property of equality & Step 2: & [tex]$500 + 375x - 500 = y - 500$[/tex] \\
3: Simplification & Step 3: & [tex]$375x = y - 500$[/tex] \\
4: Division property of equality & Step 4: & [tex]$\frac{375x}{375} = \frac{y - 500}{375}$[/tex] \\
5: Simplification & Step 5: & [tex]$x = \frac{y - 500}{375}$[/tex] \\
6: Substitution, [tex]$y = 3,500$[/tex] & Step 6: & [tex]$x = \frac{3,500 - 500}{375}$[/tex] \\
7: Simplification & Step 7: & [tex]$x = 8$[/tex] \\
\hline
\end{tabular}

Review the steps above and select the error.

Sagot :

GinnyAnsweridn
Let's go through Jerome's work step-by-step to identify any errors:

1. Equation given:
[tex]\[ 500 + 375x = y \][/tex]
Jerome correctly starts with the given equation that models his savings situation.

2. Addition property of equality:
[tex]\[ 500 + 375x - 500 = y - 500 \][/tex]
Jerome applies the addition property of equality to isolate the term containing [tex]\( x \)[/tex] on one side of the equation.

3. Simplification:
[tex]\[ 375x = y - 500 \][/tex]
Jerome simplifies both sides of the equation correctly after subtracting 500 from both sides.

4. Division property of equality:
[tex]\[ \frac{375z}{375} = \frac{y - 500}{375} \][/tex]
This step contains an error. Jerome mistakenly uses [tex]\( z \)[/tex] instead of [tex]\( x \)[/tex]. It should be:
[tex]\[ \frac{375x}{375} = \frac{y - 500}{375} \][/tex]

5. Simplification:
[tex]\[ x = \frac{y - 500}{375} \][/tex]
After correcting the variable, this step correctly simplifies the equation to solve for [tex]\( x \)[/tex].

6. Substitution, [tex]\( y = 3500 \)[/tex]:
[tex]\[ x = \frac{3500 - 500}{375} \][/tex]
Jerome substitutes 3500 for [tex]\( y \)[/tex], which is correct.

7. Simplification:
[tex]\[ x = \frac{3000}{375} = 8 \][/tex]
Jerome simplifies the fraction correctly to find that [tex]\( x \)[/tex] equals 8.

In summary, the error in Jerome's solution is in Step 4 where he uses [tex]\( z \)[/tex] instead of [tex]\( x \)[/tex]. This discrepancy is the mistake in his process. Hence, the correct error is in Step 4, and the corrected step should be:

[tex]\[ \frac{375x}{375} = \frac{y - 500}{375} \][/tex]

This ensures the variable [tex]\( x \)[/tex] is consistently used throughout the equation.
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