# Problem of the Week

## Updated at Aug 10, 2020 1:56 PM

For this week we've brought you this equation problem.

How would you solve $$\frac{5}{2+t}\times \frac{3-t}{3}=\frac{5}{12}$$?

Here are the steps:

$\frac{5}{2+t}\times \frac{3-t}{3}=\frac{5}{12}$

 1 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$\frac{5(3-t)}{(2+t)\times 3}=\frac{5}{12}$2 Regroup terms.$\frac{5(3-t)}{3(2+t)}=\frac{5}{12}$3 Multiply both sides by $$3(2+t)$$.$5(3-t)=\frac{5}{12}\times 3(2+t)$4 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$5(3-t)=\frac{5\times 3(2+t)}{12}$5 Simplify  $$5\times 3(2+t)$$  to  $$15(2+t)$$.$5(3-t)=\frac{15(2+t)}{12}$6 Simplify  $$\frac{15(2+t)}{12}$$  to  $$\frac{5(2+t)}{4}$$.$5(3-t)=\frac{5(2+t)}{4}$7 Multiply both sides by $$4$$.$20(3-t)=5(2+t)$8 Divide both sides by $$5$$.$4(3-t)=2+t$9 Expand.$12-4t=2+t$10 Add $$4t$$ to both sides.$12=2+t+4t$11 Simplify  $$2+t+4t$$  to  $$2+5t$$.$12=2+5t$12 Subtract $$2$$ from both sides.$12-2=5t$13 Simplify  $$12-2$$  to  $$10$$.$10=5t$14 Divide both sides by $$5$$.$\frac{10}{5}=t$15 Simplify  $$\frac{10}{5}$$  to  $$2$$.$2=t$16 Switch sides.$t=2$Done t=2