Question

the sum of two whole numbers is 84. if the ratio of the numbers is 2:5, find the numbers​

Answer 1

Given that:- There are 2 whole numbers whose sum is $84.$

The ratio is $2:5,$

Let, the two numbers be x and y,

So, $x-y=84...(i)$

According to the question,

$=>\frac{x}{y} =\frac{2}{5}\\=>5x=2y\\=>x= \frac{2}{5}y$

Put the value of x in equation (1) we get,

$=>\frac{2}{5} y+y=84$

Multiply both sides by 5 we get,

$=>2y-5y=84\times5\\=>-3y=420\\=>y=-140$

Substitute the value of y in equation (i),

$=>x-y=84\\=>x-(-140)=84\\=>x+140=84\\=>x=84-140\\=>x=-56$

Then, the number is -56 and -140.

Answer 2

As per give the data in the question, we have to determine the required numbers.

Given data:- Ratio-$2:5.$

Sum of two numbers=$84.$

Let, the two numbers be x and y,

So, $x-y=84 \ldots(i)$

According to the question,

$\begin{array}{l}=>\frac{x}{y}=\frac{2}{5} \\=>5 x=2 y \\=>x=\frac{2}{5} y\end{array}$

Putting the value of x in equation (1) we get,

$=>\frac{2}{5} y+y=84$

Multiply both sides by 5 we get,

$\begin{array}{l}=>2 y-5 y=84 \times 5 \\=>-3 y=420 \\=>y=-140\end{array}$

Substitute the value ofy in equation (i),

$\begin{array}{l}=>x-y=84 \\=>x-(-140)=84 \\=>x+140=84 \\=>x=84-140 \\=>x=-56\end{array}$

Hence, the number is $-56$ and $-140.$