Question

The difference of two numbers is 11. Their sum is 87. Find the numbers.

Answer 1

38 and 49

Explanation:

Let the numbers be x and y

Given that the difference of the numbers is 11, we can write:

x - y = 11 -------- (eq 1)

Also given that their sum is 87, we can write:

x + y = 87 --------(eq 2)

we now have a system of 2 equations with two unknowns.

Solving by elimination:

(eq 1) + (eq 2)

(x-y) + (x+y) = 11 + 87

x - y + x +y = 98

2x = 98 (divide both sides by 2)

x = 98/2 = 49 (answer)

substituting this into equation 2

x + y = 87

49 + y = 87 (subtract 49 from both sides)

y = 87 - 49

y = 38 (answer)

Answer 2

x = 49; y = 38

Explanation:

This can be solved with simultaneous equations;

Let the first number be x and the second be y.

If their difference is 11 then

⇒
`x - y = 11`

If their sum is 87 then

⇒
`x + y = 87`

If we add these two equations together, we can eliminate y;

⇒
`2x = 98`

⇒
`x = 49`

Now substitute into either equation;

⇒
`(49) - y = 11`

⇒
`y = 38`