Question

a number is 40% more than another number. if the sum of the two numbers is 84, find the two numbers

Answer 1

If a number is 40% more than another number, we can say that the new number is equivalent to the sum of the old number and 40% of the old number. Let's try to represent this as an equation. First, let's convert the percentage to a fraction:

$40 \% = \dfrac{40}{100} = \dfrac{2}{5}$

Defining $n$ as the new number and $o$ as the old number, we can say:

$n = o + \dfrac{2}{5} o$

Also, we can say:

$n + o = 84$

To solve, let's substitute the first equation into the second equation for $n$ and simplify.

$(o + \dfrac{2}{5} o) + o = 84$

• Substitute

$\dfrac{5o}{5} + \dfrac{2o}{5} + \dfrac{5o}{5} = 84$

• Get terms over common denominator

$\dfrac{12o}{5} = 84$

• Simplify

$12o = 420$

• Multiply both sides by 5

$o = \dfrac{420}{12} = 35$

We now have found the old number. Using the second equation we found near the beginning, let's find $n$.

$n + 35 = 84$

$n = 84 - 35 = 49$

The numbers are 35 and 49.