Question

Oliver is thinking of a number. He multiplies it by 5, subtracts 26, and then divides by 6. He then multiplies his original number by 3, and gets the same answer. Find Oliver's number.

Answer 1

-2

Explanation:

Let Oliver's number be x.

He multiplies it by 5:

x * 5 = 5x

He then subtracts 26:

5x - 26

Then, he divides by 6:

`(5x - 26)/(6)`

He then multiplies his original number by 3, and gets the same answer.

This implies that:

`(5x - 26)/(6) = 3x`

Let us simplify this:

`(5x - 26)/(6) = 3x\\\\5x - 26 = 3x * 6\\\\5x - 26 = 18x`

Collecting like terms:

`5x - 18x = 26\\\\-13x = 26\\\\=> x = (26)/(-13)\\\\x = -2`

Oliver's number is -2.