Question

r = 2.24 + 0.06x
p= 2.89 +0.10x
In the equations above, r and p represent the price per gallon, in dollars, of regular and premium grades of gasoline, respectively, x months after January 1 of last
year. What was the cost per gallon, in dollars, of premium gasoline for the month in which the per gallon price of premium exceeded
the per gallon price of regular by $0.93? Please explain thoroughly

Answer 1

Based on the equations of the price, the price of the premium gasoline, p = $3.59

What is the equation of the prices?

An equation is an expression that describes two quantities as being equal.

The equation of the different prices of gasoline is given below:

• Price of regular grade of gasoline, r = 2.24 + 0.06x
• Price of premium grade of gasoline, p = 2.89 + 0.10x

Where x is the number of months after January 1 of last year.

When the per gallon price of premium exceeded the per gallon price of regular by $0.93, the two equations will be related as shown below:

p = r + 0.93 ---- (3)

r + 0.93 = 0.93 + 2.24 + 0.06x

r + 0.93 = 3.17 + 0.06x

Therefore, p = 3.17 + 0.06x --- (4)

Also, p = 2.89 +0.10 x --- (2)

solving for x by equating (1) and (4)

3.17 + 0.06x = 2.89 + 0.10x

0.10x - 0.06x = 3.17 - 2.89

0.04x = 0.28

x = 7

Then, substituting for x in (4)

p = 3.17 + 0.06 * 7

p = $3.59

In conclusion, the price of the premium gasoline is determined from the given equations of the price.

Learn more about equations at: https://brainly.com/question/22688504

#SPJ1