Answer :
Certainly! Let's go through Penny's work step-by-step to see if she solved the equation correctly.
The original equation given is:
[tex]\[
\frac{3}{5} y - 8 = 4
\][/tex]
Step 1: Add 8 to both sides
To isolate the term with [tex]\(y\)[/tex], we first add 8 to both sides of the equation:
[tex]\[
\frac{3}{5} y - 8 + 8 = 4 + 8
\][/tex]
Simplifying both sides gives:
[tex]\[
\frac{3}{5} y = 12
\][/tex]
Step 2: Multiply both sides by [tex]\(\frac{5}{3}\)[/tex]
To solve for [tex]\(y\)[/tex], we need to get rid of the fraction [tex]\(\frac{3}{5}\)[/tex] that is multiplying [tex]\(y\)[/tex]. We can do this by multiplying both sides of the equation by the reciprocal, which is [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[
\left(\frac{5}{3}\right) \cdot \frac{3}{5} y = 12 \cdot \frac{5}{3}
\][/tex]
On the left side, the [tex]\(\frac{5}{3} \cdot \frac{3}{5}\)[/tex] simplifies to 1, leaving:
[tex]\[
y = 12 \cdot \frac{5}{3}
\][/tex]
Step 3: Calculate the value of [tex]\(y\)[/tex]
Now, we simplify the right side:
[tex]\[
y = \frac{12 \times 5}{3} = \frac{60}{3} = 20
\][/tex]
Therefore, [tex]\(y = 20\)[/tex].
Conclusion:
Penny's calculations are correct, and the solution to the equation is indeed [tex]\(y = 20\)[/tex]. Thus, she solved the equation correctly.
The original equation given is:
[tex]\[
\frac{3}{5} y - 8 = 4
\][/tex]
Step 1: Add 8 to both sides
To isolate the term with [tex]\(y\)[/tex], we first add 8 to both sides of the equation:
[tex]\[
\frac{3}{5} y - 8 + 8 = 4 + 8
\][/tex]
Simplifying both sides gives:
[tex]\[
\frac{3}{5} y = 12
\][/tex]
Step 2: Multiply both sides by [tex]\(\frac{5}{3}\)[/tex]
To solve for [tex]\(y\)[/tex], we need to get rid of the fraction [tex]\(\frac{3}{5}\)[/tex] that is multiplying [tex]\(y\)[/tex]. We can do this by multiplying both sides of the equation by the reciprocal, which is [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[
\left(\frac{5}{3}\right) \cdot \frac{3}{5} y = 12 \cdot \frac{5}{3}
\][/tex]
On the left side, the [tex]\(\frac{5}{3} \cdot \frac{3}{5}\)[/tex] simplifies to 1, leaving:
[tex]\[
y = 12 \cdot \frac{5}{3}
\][/tex]
Step 3: Calculate the value of [tex]\(y\)[/tex]
Now, we simplify the right side:
[tex]\[
y = \frac{12 \times 5}{3} = \frac{60}{3} = 20
\][/tex]
Therefore, [tex]\(y = 20\)[/tex].
Conclusion:
Penny's calculations are correct, and the solution to the equation is indeed [tex]\(y = 20\)[/tex]. Thus, she solved the equation correctly.
