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Answer :
Sure! Let's solve Penny's problem step by step to see if she has done it correctly.
### Step-by-Step Solution:
Line 1:
[tex]\[
\frac{3}{5} y - 8 = 4
\][/tex]
1. Add 8 to both sides:
To isolate the term with [tex]\( y \)[/tex], add 8 to both sides of the equation:
[tex]\[
\frac{3}{5} y - 8 + 8 = 4 + 8
\][/tex]
[tex]\[
\frac{3}{5} y = 12
\][/tex]
2. Multiply by the reciprocal:
Multiply both sides by the reciprocal of [tex]\( \frac{3}{5} \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 12 \times \frac{5}{3}
\][/tex]
[tex]\[
y = 20
\][/tex]
Penny correctly finds [tex]\( y = 20 \)[/tex] from Line 1.
Line 2:
[tex]\[
\frac{5}{3} \cdot \frac{3}{5} y = 12 \cdot \frac{5}{3}
\][/tex]
1. Simplify the left side:
[tex]\(\frac{5}{3} \times \frac{3}{5} y\)[/tex] simplifies to [tex]\(y\)[/tex] because [tex]\(\frac{5}{3} \times \frac{3}{5} = 1\)[/tex].
2. Simplify the right side:
Calculate [tex]\( 12 \times \frac{5}{3} \)[/tex]:
[tex]\[
12 \times \frac{5}{3} = 20
\][/tex]
So, the equation simplifies to:
[tex]\[
y = 20
\][/tex]
Penny also finds [tex]\( y = 20 \)[/tex] correctly in Line 2.
Conclusion:
Penny solved both equations correctly, and both approaches lead to the same solution:
[tex]\( y = 20 \)[/tex]
### Step-by-Step Solution:
Line 1:
[tex]\[
\frac{3}{5} y - 8 = 4
\][/tex]
1. Add 8 to both sides:
To isolate the term with [tex]\( y \)[/tex], add 8 to both sides of the equation:
[tex]\[
\frac{3}{5} y - 8 + 8 = 4 + 8
\][/tex]
[tex]\[
\frac{3}{5} y = 12
\][/tex]
2. Multiply by the reciprocal:
Multiply both sides by the reciprocal of [tex]\( \frac{3}{5} \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 12 \times \frac{5}{3}
\][/tex]
[tex]\[
y = 20
\][/tex]
Penny correctly finds [tex]\( y = 20 \)[/tex] from Line 1.
Line 2:
[tex]\[
\frac{5}{3} \cdot \frac{3}{5} y = 12 \cdot \frac{5}{3}
\][/tex]
1. Simplify the left side:
[tex]\(\frac{5}{3} \times \frac{3}{5} y\)[/tex] simplifies to [tex]\(y\)[/tex] because [tex]\(\frac{5}{3} \times \frac{3}{5} = 1\)[/tex].
2. Simplify the right side:
Calculate [tex]\( 12 \times \frac{5}{3} \)[/tex]:
[tex]\[
12 \times \frac{5}{3} = 20
\][/tex]
So, the equation simplifies to:
[tex]\[
y = 20
\][/tex]
Penny also finds [tex]\( y = 20 \)[/tex] correctly in Line 2.
Conclusion:
Penny solved both equations correctly, and both approaches lead to the same solution:
[tex]\( y = 20 \)[/tex]
Thanks for taking the time to read Penny s solving work is shown here Has she solved this equation correctly Line 1 tex quad frac 3 5 y 8 4 tex Line. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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Rewritten by : Barada
