Question

From 5 times a certain number, 189 is subtracted, and the remainder is one half the original number. What is that number?

Answer 1

Let x be the unknown number. 5 times that number means 5x. If we subtract 189 from this number, we get 5x-189.

Also, half the original number is x/2.

The two operations output the same result, so we have the following equation:

`5x-189 = (x)/(2)`

Subtract x/2 from both sides and add 189 to both sides to get

`5x-(x)/(2)=189 \iff (9x)/(2)=189`

Multiply both sides by 2 to get

`9x=378`

Finally, divide both sides by 9:

`x = (378)/(9)=42`