Question

Sum of two numbers is 29 and one number exceeds another by 5. Find the numbers.

Answer 1

Hint: Given, the sum of two numbers is 29. One number exceeds another by 5. We need to find those two numbers. Since one number exceeds another, one will be smaller compared to another. Let the smaller number be \[x \] and the larger number will be \[y \] . Using the given condition we will create an equation and we will solve it.

Complete step-by-step answer:
Let the smaller number be \[x \] .
The larger number will be \[y \] .
As per the given question the sum of two numbers is 25.
 \[ \Rightarrow x + y = 29 \] --- (1)
Also, given one of the numbers, that is \[y \] exceeds the other by 9.
 \[ \Rightarrow y = x + 5 \] ---- (2)
Substituting equation (2) in equation (1), we get:
 \[ \Rightarrow x + y = 29 \]
 \[ \Rightarrow x + x + 5 = 29 \] (Adding variables)
 \[ \Rightarrow 2x + 5 = 29 \]
 (Rearranging so that variables will be on one side and constant on the other side.)
 \[ \Rightarrow 2x = 29 - 5 \]
 \[ \Rightarrow 2x = 24 \] (Divide both side by 2)
 \[ \Rightarrow x = \dfrac{{24}}{2} \]
 \[ \Rightarrow x = 12 \]
We get the smaller number, to find the larger number we will substitute \[x \] in equation (2) we get:
 \[ \Rightarrow y = x + 5 \] (On substituting)
 \[ \Rightarrow y = 12 + 5 \]
 \[ \Rightarrow y = 17 \]
We can check this answer by substituting \[x \] and \[y \] in the equation (1).
That is, \[ \Rightarrow 12 + 17 = 29 \]
 \[ \Rightarrow 12 + 17 = 29 \]
 \[ \Rightarrow 29 = 29 \] .That we have obtained the correct answer.
So, the correct answer is “x=12,y=17”.

Note: All we did is convert the given word problem into an algebraic equation. Since 29 is a small number you can guess the answer by trial and error method, although not the best strategy. You can also solve this problem directly by using the equation (1) and the equation (2) and solving using the system of equation method.