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(5−32+y)=6653(5-\frac{3}{2+y})=\frac{66}{5}?

Let's begin!



3(5−32+y)=6653(5-\frac{3}{2+y})=\frac{66}{5}

1
Divide both sides by 33.
5−32+y=66535-\frac{3}{2+y}=\frac{\frac{66}{5}}{3}

2
Simplify  6653\frac{\frac{66}{5}}{3}  to  665×3\frac{66}{5\times 3}.
5−32+y=665×35-\frac{3}{2+y}=\frac{66}{5\times 3}

3
Simplify  5×35\times 3  to  1515.
5−32+y=66155-\frac{3}{2+y}=\frac{66}{15}

4
Simplify  6615\frac{66}{15}  to  225\frac{22}{5}.
5−32+y=2255-\frac{3}{2+y}=\frac{22}{5}

5
Subtract 55 from both sides.
−32+y=225−5-\frac{3}{2+y}=\frac{22}{5}-5

6
Simplify  225−5\frac{22}{5}-5  to  −35-\frac{3}{5}.
−32+y=−35-\frac{3}{2+y}=-\frac{3}{5}

7
Multiply both sides by 2+y2+y.
−3=−35(2+y)-3=-\frac{3}{5}(2+y)

8
Simplify  35(2+y)\frac{3}{5}(2+y)  to  3(2+y)5\frac{3(2+y)}{5}.
−3=−3(2+y)5-3=-\frac{3(2+y)}{5}

9
Multiply both sides by 55.
−3×5=−3(2+y)-3\times 5=-3(2+y)

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

11
Divide both sides by −3-3.
−15−3=2+y\frac{-15}{-3}=2+y

12
Two negatives make a positive.
153=2+y\frac{15}{3}=2+y

13
Simplify  153\frac{15}{3}  to  55.
5=2+y5=2+y

14
Subtract 22 from both sides.
5−2=y5-2=y

15
Simplify  5−25-2  to  33.
3=y3=y

16
Switch sides.
y=3y=3

Done
Cymath foriOSAndroid