Problem of the Week

Updated at Feb 4, 2019 2:47 PM

How would you solve t−33+23=89\frac{\frac{t-3}{3}+2}{3}=\frac{8}{9}?

Below is the solution.



t−33+23=89\frac{\frac{t-3}{3}+2}{3}=\frac{8}{9}

1
Simplify  t−33\frac{t-3}{3}  to  −1+t3-1+\frac{t}{3}.
−1+t3+23=89\frac{-1+\frac{t}{3}+2}{3}=\frac{8}{9}

2
Simplify  −1+t3+2-1+\frac{t}{3}+2  to  t3+1\frac{t}{3}+1.
t3+13=89\frac{\frac{t}{3}+1}{3}=\frac{8}{9}

3
Simplify  t3+13\frac{\frac{t}{3}+1}{3}  to  t33+13\frac{\frac{t}{3}}{3}+\frac{1}{3}.
t33+13=89\frac{\frac{t}{3}}{3}+\frac{1}{3}=\frac{8}{9}

4
Simplify  t33\frac{\frac{t}{3}}{3}  to  t3×3\frac{t}{3\times 3}.
t3×3+13=89\frac{t}{3\times 3}+\frac{1}{3}=\frac{8}{9}

5
Simplify  3×33\times 3  to  99.
t9+13=89\frac{t}{9}+\frac{1}{3}=\frac{8}{9}

6
Subtract 13\frac{1}{3} from both sides.
t9=89−13\frac{t}{9}=\frac{8}{9}-\frac{1}{3}

7
Simplify  89−13\frac{8}{9}-\frac{1}{3}  to  59\frac{5}{9}.
t9=59\frac{t}{9}=\frac{5}{9}

8
Multiply both sides by 99.
t=59×9t=\frac{5}{9}\times 9

9
Cancel 99.
t=5t=5

Done
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