Problem of the Week

Updated at Jan 20, 2025 8:55 AM

This week's problem comes from the equation category.

How would you solve the equation \(3(5-\frac{3}{2+y})=\frac{66}{5}\)?

Let's begin!



\[3(5-\frac{3}{2+y})=\frac{66}{5}\]

1
Divide both sides by \(3\).
\[5-\frac{3}{2+y}=\frac{\frac{66}{5}}{3}\]

2
Simplify  \(\frac{\frac{66}{5}}{3}\)  to  \(\frac{66}{5\times 3}\).
\[5-\frac{3}{2+y}=\frac{66}{5\times 3}\]

3
Simplify  \(5\times 3\)  to  \(15\).
\[5-\frac{3}{2+y}=\frac{66}{15}\]

4
Simplify  \(\frac{66}{15}\)  to  \(\frac{22}{5}\).
\[5-\frac{3}{2+y}=\frac{22}{5}\]

5
Subtract \(5\) from both sides.
\[-\frac{3}{2+y}=\frac{22}{5}-5\]

6
Simplify  \(\frac{22}{5}-5\)  to  \(-\frac{3}{5}\).
\[-\frac{3}{2+y}=-\frac{3}{5}\]

7
Multiply both sides by \(2+y\).
\[-3=-\frac{3}{5}(2+y)\]

8
Simplify  \(\frac{3}{5}(2+y)\)  to  \(\frac{3(2+y)}{5}\).
\[-3=-\frac{3(2+y)}{5}\]

9
Multiply both sides by \(5\).
\[-3\times 5=-3(2+y)\]

10
Simplify  \(-3\times 5\)  to  \(-15\).
\[-15=-3(2+y)\]

11
Divide both sides by \(-3\).
\[\frac{-15}{-3}=2+y\]

12
Two negatives make a positive.
\[\frac{15}{3}=2+y\]

13
Simplify  \(\frac{15}{3}\)  to  \(5\).
\[5=2+y\]

14
Subtract \(2\) from both sides.
\[5-2=y\]

15
Simplify  \(5-2\)  to  \(3\).
\[3=y\]

16
Switch sides.
\[y=3\]

Done
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