# Problem of the Week

Updated at Feb 4, 2019 2:47 PM

How would you solve $$\frac{\frac{t-3}{3}+2}{3}=\frac{8}{9}$$?

Below is the solution.

$\frac{\frac{t-3}{3}+2}{3}=\frac{8}{9}$

 1 Simplify $$\frac{t-3}{3}$$ to $$-1+\frac{t}{3}$$.$\frac{-1+\frac{t}{3}+2}{3}=\frac{8}{9}$2 Simplify $$-1+\frac{t}{3}+2$$ to $$\frac{t}{3}+1$$.$\frac{\frac{t}{3}+1}{3}=\frac{8}{9}$3 Simplify $$\frac{\frac{t}{3}+1}{3}$$ to $$\frac{\frac{t}{3}}{3}+\frac{1}{3}$$.$\frac{\frac{t}{3}}{3}+\frac{1}{3}=\frac{8}{9}$4 Simplify $$\frac{\frac{t}{3}}{3}$$ to $$\frac{t}{3\times 3}$$.$\frac{t}{3\times 3}+\frac{1}{3}=\frac{8}{9}$5 Simplify $$3\times 3$$ to $$9$$.$\frac{t}{9}+\frac{1}{3}=\frac{8}{9}$6 Subtract $$\frac{1}{3}$$ from both sides.$\frac{t}{9}=\frac{8}{9}-\frac{1}{3}$7 Simplify $$\frac{8}{9}-\frac{1}{3}$$ to $$\frac{5}{9}$$.$\frac{t}{9}=\frac{5}{9}$8 Multiply both sides by $$9$$.$t=\frac{5}{9}\times 9$9 Simplify $$\frac{5}{9}\times 9$$ to $$\frac{45}{9}$$.$t=\frac{45}{9}$10 Simplify $$\frac{45}{9}$$ to $$5$$.$t=5$Donet=5