Problem of the Week

Updated at Sep 27, 2021 1:30 PM

This week's problem comes from the equation category.

How can we solve the equation 45t−t−35=3\frac{4}{5}t-\frac{t-3}{5}=3?

Let's begin!



45t−t−35=3\frac{4}{5}t-\frac{t-3}{5}=3

1
Simplify  45t\frac{4}{5}t  to  4t5\frac{4t}{5}.
4t5−t−35=3\frac{4t}{5}-\frac{t-3}{5}=3

2
Join the denominators.
4t−(t−3)5=3\frac{4t-(t-3)}{5}=3

3
Remove parentheses.
4t−t+35=3\frac{4t-t+3}{5}=3

4
Simplify  4t−t+34t-t+3  to  3t+33t+3.
3t+35=3\frac{3t+3}{5}=3

5
Factor out the common term 33.
3(t+1)5=3\frac{3(t+1)}{5}=3

6
Multiply both sides by 55.
3(t+1)=3×53(t+1)=3\times 5

7
Simplify  3×53\times 5  to  1515.
3(t+1)=153(t+1)=15

8
Divide both sides by 33.
t+1=153t+1=\frac{15}{3}

9
Simplify  153\frac{15}{3}  to  55.
t+1=5t+1=5

10
Subtract 11 from both sides.
t=5−1t=5-1

11
Simplify  5−15-1  to  44.
t=4t=4

Done
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