Question

Two positive numbers have a difference of 21. The larger number is five more than twice the smaller. Find the two numbers.

Answer 1

Let n = the smaller of the two numbers, and since the other number is 5 more than twice the smaller number n, then ...

Let 2n + 5 = the second and larger number.

Since the sum of the two unknown numbers is 26, then we can write the following equation to be solved for n as follows:
n + (2n + 5) = 26

n + 2n + 5 = 26

Collecting like-terms on the left, we get:
3n + 5 = 26

3n + 5 - 5 = 26 - 5

3n + 0 = 21

3n = 21

(3n)/3 = 21/3

(3/3)n = 21/3

(1)n = 7

n = 7

Therefore, ...
2n + 5 = 2(7) + 5
= 14 + 5
= 19

CHECK:
n + (2n + 5) = 26
7 + (19) = 26
7 + 19 = 26
26 = 26

Therefore, the two desired numbers whose sum is 26 are indeed 7 and 19.

Hope this helps :)