# Problem of the Week

## Updated at Feb 21, 2022 1:48 PM

This week we have another equation problem:

How can we solve the equation $$\frac{5}{5+\frac{4}{4z}}=\frac{25}{26}$$?

Let's start!

$\frac{5}{5+\frac{4}{4z}}=\frac{25}{26}$

 1 Cancel $$4$$.$\frac{5}{5+\frac{1}{z}}=\frac{25}{26}$2 Multiply both sides by $$5+\frac{1}{z}$$.$5=\frac{25}{26}(5+\frac{1}{z})$3 Divide both sides by $$25$$.$\frac{5}{25}=\frac{1}{26}(5+\frac{1}{z})$4 Simplify  $$\frac{5}{25}$$  to  $$\frac{1}{5}$$.$\frac{1}{5}=\frac{1}{26}(5+\frac{1}{z})$5 Simplify  $$\frac{5+\frac{1}{z}}{26}$$  to  $$\frac{5}{26}+\frac{\frac{1}{z}}{26}$$.$\frac{1}{5}=\frac{5}{26}+\frac{\frac{1}{z}}{26}$6 Simplify  $$\frac{\frac{1}{z}}{26}$$  to  $$\frac{1}{26z}$$.$\frac{1}{5}=\frac{5}{26}+\frac{1}{26z}$7 Subtract $$\frac{5}{26}$$ from both sides.$\frac{1}{5}-\frac{5}{26}=\frac{1}{26z}$8 Simplify  $$\frac{1}{5}-\frac{5}{26}$$  to  $$\frac{1}{130}$$.$\frac{1}{130}=\frac{1}{26z}$9 Multiply both sides by $$26z$$.$\frac{1}{130}\times 26z=1$10 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$\frac{1\times 26z}{130}=1$11 Simplify  $$1\times 26z$$  to  $$26z$$.$\frac{26z}{130}=1$12 Simplify  $$\frac{26z}{130}$$  to  $$\frac{z}{5}$$.$\frac{z}{5}=1$13 Multiply both sides by $$5$$.$z=1\times 5$14 Simplify  $$1\times 5$$  to  $$5$$.$z=5$Donez=5