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:

$5x-189 = \dfrac{x}{2}$

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

$5x-\dfrac{x}{2}=189 \iff \dfrac{9x}{2}=189$

Multiply both sides by 2 to get

$9x=378$

Finally, divide both sides by 9:

$x = \dfrac{378}{9}=42$