Question

When a number is decreased by 20% of itself, the result is 40. What is the number?a) Write an equation to model the problem. Use x to represent the number.Answer: 40 = 8xAb) Solve the equation to find the number:Answer: 54

Answer 1

From the statement of the problem, we know that the number x is decreased by 20% of itself, and the result is 40.

a) To write an equation for the problem, we take into account that the 20% of a number is equal to the number multiplied by 20 and divided by 100. According to the statement: we have a number x that is decreased by 20% of itself ( x * 20/100) and it is equal to 40, we can write this as:

$x-x\cdot\frac{20}{100}=40.$

We can also rewrite this equation in the following way:

$\begin{gathered} x-0.2x=40, \\ 0.8x=40. \end{gathered}$

b) We solve the equation of the problem by the following steps:

$\begin{gathered} x=\frac{40}{0.8}, \\ x=50. \end{gathered}$

So the solution is x = 50. We can verify this is solution computing the 20% of 50, which is 10 and subtracting that to 50 we get 40, which is required by the statement.