# Problem of the Week

## Updated at Mar 30, 2020 11:07 AM

How would you solve the equation $$5+\frac{2}{5+\frac{5}{t}}=\frac{26}{5}$$?

Below is the solution.

$5+\frac{2}{5+\frac{5}{t}}=\frac{26}{5}$

 1 Factor out the common term $$5$$.$5+\frac{2}{5(1+\frac{1}{t})}=\frac{26}{5}$2 Subtract $$5$$ from both sides.$\frac{2}{5(1+\frac{1}{t})}=\frac{26}{5}-5$3 Simplify  $$\frac{26}{5}-5$$  to  $$\frac{1}{5}$$.$\frac{2}{5(1+\frac{1}{t})}=\frac{1}{5}$4 Multiply both sides by $$5(1+\frac{1}{t})$$.$2=\frac{1}{5}\times 5(1+\frac{1}{t})$5 Cancel $$5$$.$2=1+\frac{1}{t}$6 Subtract $$1$$ from both sides.$2-1=\frac{1}{t}$7 Simplify  $$2-1$$  to  $$1$$.$1=\frac{1}{t}$8 Multiply both sides by $$t$$.$t=1$Donet=1