Question

Two numbers are in the ratio $7:2$ . If their sum is 54, find the numbers.

Answer 1

Hint: We are given the ratio of two numbers. The sum of the 2 numbers is also given. We can multiply the ratio with a common variable and equate its sum to the given sum of the numbers. Then we can solve for the variable and multiply its value in the ratio to get the required number.

Complete step-by-step answer:
We are given that two numbers are in the ratio $7:2$ .
So we can write the numbers as multiple of the ratio.
Let the numbers be $7x$ and $2x$ , where x is a variable.
It is given that the sum of the two numbers is 54. So we can write it as,
 $ \Rightarrow 7x + 2x = 54$
On adding the terms in the LHS, we get,
 $ \Rightarrow 9x = 54$
On dividing throughout with 9, we get,
 \[ \Rightarrow x = \dfrac{{54}}{9}\]
 \[ \Rightarrow x = 6\]
Now we have the value of x. To get the numbers, we can substitute the value of x.
 $ \Rightarrow 7x = 7 \times 6 = 42$
 $ \Rightarrow 2x = 2 \times 6 = 12$
Therefore the required numbers are 42 and 12.

Note: Ratios are used expressing how much one quantity there is compared to other quantity. A ratio can be multiplied or divided by the same values. This property of ratio is used to solve this problem. We can check whether our answer is correct or not by taking the sum of the numbers and comparing with the given sum. We must use the same variable to multiply both sides of the ratio.