Question

A number, one fourth of that number and one fifth of that number are added. The result is 29 . What is the original number?

Answer 1

original number (x) = 20

Explanation:

x + 1/4x + 1/5x = 29

Combine like terms, so add 1, 1/4, and 1/5 together.

In order to add 1/4 and 1/5 together, we must find the common denominator, which here is 20

1/4 x 5/5 = 5/20

1/5 x 4/4 = 4/20

4/20 + 5/20 = 9/20

add 1 and 9/20 together

1 + 9/20 = 1 9/20

simplify if needed

* no simplification

* we are not done yet, we must find x

* to make it easier, we will put 1 9/20 into an improper fraction

1 x 20 = 20 + 9 = 29/20

29/20x = 29

*two step equation

29/20x times 20 = 29x

29 x 20 = 580

29x = 580

*divide

29x/29 = 580/29

x = 20

Answer 2

The number is 20.

Explanation:

Let x = the unknown number.

x + x/4 + x/5 = 29

The LCD is 20.

Multiply both sides by 20.

20x + 20 × x/4 + 20 × x/5 = 580

20x + 5x + 4x = 580

29x = 580

x = 20

Answer: The number is 20.