Question

If 120% of a is equal to 80% of b, and a=12, then what is the value of a+b?

Answer 1

Percent means parts out of 100
120%=120/100=1.2
80%=80/100=0.8
'of' means multiply

1.2 times a=0.8 times b
a=12
1.2 times 12=0.8 times b
14.4=0.8 times b
divide both sides by 0.8
18=b

so
a=12
b=18
a+b=12+18=30

Answer 2

So,

120% is the same as 1.2 or 6/5.  80% is the same as 0.8 or 4/5.

We are given the value of a, which is 12.

6/5 of a, or 1.2 times a, is equal to 4/5 of b, or 4/5 times b.

$\frac{6}{5} (12)= \frac{4}{5} b$

Simplify.

$\frac{72}{5}= \frac{4}{5} b$

Multiply both sides by 5/4.

$\frac{72}{4}\ or\ 18= b$

Therefore, the sum of a and b is 12 + 18 = 30.