Question

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

Answer 1

The task can be expressed in a following equation:

120%*a=80%*b
1.20a=0.80b
1.2a=0.8b
12a=8b
3a=2b

1) in terms of a:
3a=2b
b=3a/2=1.5a
a+b=a+1.5a=2.5a

2) in terms of b:
3a=2b
a=2/3b
a+b=2/3b+b=$1\frac{2}{3}b$

Answer 2

Answer

As per the statement:

If 120% of a is equal to 80% of b.

"120% of a" means $\frac{120}{100} \times a$

"80% of b" means $\frac{80}{100} \times b$

then;

$\frac{120}{100} \times a =\frac{80}{100} \times b$

Multiply both sides by 100 we get;

$120 \times a =\80\times b$

Divide both sides by 80 we have;

$\frac{120}{80}a = b$

Simplify:

$\frac{3}{2}a = b$        .....[1]

or

$a = \frac{2}{3} b$    ......[2]

We have to find the value of a+b in terms of a and b:

Substitute the values of [1] we have;

$a+b = a+\frac{3}{2}a$

Combine like terms;

$a+b = \frac{5}{2}a$

Now, find the value of a+b in terms of b;

Substitute equation [2] we have;

$a+b = \frac{2}{3}b+b$

Combine like terms;

$a+b =\frac{5}{3}b$

Therefore, the value of a+b in terms of a and b are;

$a+b = \frac{5}{2}a$

$a+b =\frac{5}{3}b$