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(2)/(3)b`

Answer 2

As per the statement:

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

"120% of a" means
`(120)/(100) * a`

"80% of b" means
`(80)/(100) * b`

then;

`(120)/(100) * a =(80)/(100) * b`

Multiply both sides by 100 we get;

`120 * a =\80* b`

Divide both sides by 80 we have;

`(120)/(80)a = b`

Simplify:

`(3)/(2)a = b` .....[1]

or

`a = (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+(3)/(2)a`

Combine like terms;

`a+b = (5)/(2)a`

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

Substitute equation [2] we have;

`a+b = (2)/(3)b+b`

Combine like terms;

`a+b =(5)/(3)b`

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

`a+b = (5)/(2)a`

`a+b =(5)/(3)b`