To solve the given problem, let's analyze each step in Peter's procedure and identify the appropriate mathematical properties he used.
Step-by-Step Solution:
1. Step 1: [tex]\( y = 30,000 + 2,000x \)[/tex]
Peter starts with an equation that models his savings plan where [tex]\( y \)[/tex] represents the total savings and [tex]\( x \)[/tex] represents the number of months. He currently has \[tex]$30,000 saved and saves an additional \$[/tex]2,000 per month.
2. Step 2: [tex]\( y - 30,000 = 30,000 + 2,000x - 30,000 \)[/tex]
Peter subtracts \$30,000 from both sides of the equation. This is applying the subtraction property of equality.
3. Step 3: [tex]\( y - 30,000 = 2,000x \)[/tex]
By simplifying the expression [tex]\( 30,000 + 2,000x - 30,000 \)[/tex] on the right side, Peter shows that [tex]\( y - 30,000 = 2,000x \)[/tex].
4. Step 4: [tex]\( \frac{y - 30,000}{2,000} = \frac{2,000x}{2,000} \)[/tex]
Here, Peter divides both sides of the equation [tex]\( y - 30,000 = 2,000x \)[/tex] by 2,000. This is applying the division property of equality.
5. Step 5: [tex]\( \frac{y - 30,000}{2,000} = x \)[/tex]
Simplifying the right side of the equation [tex]\( \frac{2,000x}{2,000} \)[/tex] to get [tex]\( x \)[/tex], Peter shows the equation in terms of [tex]\( x \)[/tex].
6. Step 6: [tex]\( \frac{50,000 - 30,000}{2,000} = x \)[/tex]
Peter substitutes [tex]\( y = 50,000 \)[/tex] (his savings goal) into the equation to determine the number of months [tex]\( x \)[/tex] required to reach this goal. This uses the substitution property.
7. Step 7: [tex]\( 10 = x \)[/tex]
After performing the arithmetic [tex]\( \frac{20,000}{2,000} = 10 \)[/tex], Peter finds that it will take 10 months to reach his savings goal.
Correct Answer:
A. Peter used the division property of equality in step 4.
So, the answer is:
[tex]\( (10.0, 'A') \)[/tex]
Thus, Peter used the division property of equality in step 4.
