If 120% of a is equal to 80% of b, then what is the value of a+b in terms of a and b?
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
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;
\(a+b = \frac{5}{2}a\)
\(a+b =\frac{5}{3}b\)