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 52+t×3−t3=512\frac{5}{2+t}\times \frac{3-t}{3}=\frac{5}{12}?

Here are the steps:



52+t×3−t3=512\frac{5}{2+t}\times \frac{3-t}{3}=\frac{5}{12}

1
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
5(3−t)(2+t)×3=512\frac{5(3-t)}{(2+t)\times 3}=\frac{5}{12}

2
Regroup terms.
5(3−t)3(2+t)=512\frac{5(3-t)}{3(2+t)}=\frac{5}{12}

3
Multiply both sides by 3(2+t)3(2+t).
5(3−t)=512×3(2+t)5(3-t)=\frac{5}{12}\times 3(2+t)

4
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
5(3−t)=5×3(2+t)125(3-t)=\frac{5\times 3(2+t)}{12}

5
Simplify  5×3(2+t)5\times 3(2+t)  to  15(2+t)15(2+t).
5(3−t)=15(2+t)125(3-t)=\frac{15(2+t)}{12}

6
Simplify  15(2+t)12\frac{15(2+t)}{12}  to  5(2+t)4\frac{5(2+t)}{4}.
5(3−t)=5(2+t)45(3-t)=\frac{5(2+t)}{4}

7
Multiply both sides by 44.
20(3−t)=5(2+t)20(3-t)=5(2+t)

8
Divide both sides by 55.
4(3−t)=2+t4(3-t)=2+t

9
Expand.
12−4t=2+t12-4t=2+t

10
Add 4t4t to both sides.
12=2+t+4t12=2+t+4t

11
Simplify  2+t+4t2+t+4t  to  2+5t2+5t.
12=2+5t12=2+5t

12
Subtract 22 from both sides.
12−2=5t12-2=5t

13
Simplify  12−212-2  to  1010.
10=5t10=5t

14
Divide both sides by 55.
105=t\frac{10}{5}=t

15
Simplify  105\frac{10}{5}  to  22.
2=t2=t

16
Switch sides.
t=2t=2

Done
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