Question

In a certain year, the price of gasoline rose by 20% during January, fell by 20% during February, rose by 25% in March, and fell by x % in April. The price of gasoline at the end of April was the same as it had been at the beginning of January. Find the value of x.

Answer 1

Using decimal multipliers, it is found that the value of x is of 16.67.

What is a decimal multiplier?

Increases of a% or decreases of a% re represented by decimal values, as follows:

• The equivalent multiplier for an increase of a% is given by: $\frac{100 + a}{100}$

• The equivalent multiplier for an decrease of a% is given by: $\frac{100 - a}{100}$

In this problem:

• The price at the beginning of January was of a.

• Increase of 20% in January, hence $1.2a$.

• Decrease of 20% in February, hence $1.2(0.8)a$.

• Increase of 25% in March, hence $1.2(0.8)(1.25)a$.

• Decrease of x% in April, hence $1.2(0.8)(1.25)\left(\frac{100 - x}{100}\right)a$

The price of gasoline at the end of April was the same as it had been at the beginning of January, hence:

$a =1.2(0.8)(1.25)\left(\frac{100 - x}{100}\right)a$

$1.2\left(\frac{100 - x}{100}\right) = 1$

$\left(\frac{100 - x}{100}\right) = \frac{1}{1.2}$

$\frac{100 - x}{100} = 0.8333$

$100 - x = 83.33$

$x = 16.67$

The value of x is of 16.67.

To learn more about decimal multipliers, you can take a look at brainly.com/question/24952336