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: [tex]\frac{100 + a}{100}[/tex]
- The equivalent multiplier for an decrease of a% is given by: [tex]\frac{100 - a}{100}[/tex]
In this problem:
- The price at the beginning of January was of a.
- Increase of 20% in January, hence [tex]1.2a[/tex].
- Decrease of 20% in February, hence [tex]1.2(0.8)a[/tex].
- Increase of 25% in March, hence [tex]1.2(0.8)(1.25)a[/tex].
- Decrease of x% in April, hence [tex]1.2(0.8)(1.25)\left(\frac{100 - x}{100}\right)a[/tex]
The price of gasoline at the end of April was the same as it had been at the beginning of January, hence:
[tex]a =1.2(0.8)(1.25)\left(\frac{100 - x}{100}\right)a[/tex]
[tex]1.2\left(\frac{100 - x}{100}\right) = 1[/tex]
[tex]\left(\frac{100 - x}{100}\right) = \frac{1}{1.2}[/tex]
[tex]\frac{100 - x}{100} = 0.8333[/tex]
[tex]100 - x = 83.33[/tex]
[tex]x = 16.67[/tex]
The value of x is of 16.67.
To learn more about decimal multipliers, you can take a look at https://brainly.com/question/24952336
