Question

Sum of two numbers is 15, their difference is 7. What are the numbers?
Let the numbers bey
Sum
15
Difference
-
(x+y)+(x-y)
23
Numbers​

Answer 1

Answer:

Let the numbers be a and b. Then according to the question,

a+b=15(1)

a−b=7(2)

As we can see, in equation 1, b is added to a and in equation 2, b is subtracted from a, so we add the two equations so that b eliminates and there is only a to work out the value. After adding we get

2a=22⟹a=11

Choosing any one equation between 1 and 2, we can find the value of b. Using equation 1,

a+b=15⟹11+b=15⟹b=15−11=4

Using equation 2,

a−b=7⟹11−b=7⟹b=11−7=4

Thus we conclude that a = 11 and b = 4.

Verify: Sum of the numbers = 11 + 4 = 15

Difference between the numbers = 11 — 4 = 7

Since the conditions matches with problem, our answer is correct. a = 11 and b = 4.