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
Cymath foriOSAndroid