SOLUTION: A gas station attendant looks over yesterday's sales report. She finds that 450 liters of regular and 320 liters of unleaded were sold for a total of $384.83. Regular was 5 cents

Question 9840: A gas station attendant looks over yesterday's sales report. She finds that 450 liters of regular and 320 liters of unleaded were sold for a total of $384.83. Regular was 5 cents per liter cheaper than unleaded. What were the two prices per liter yesterday?
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
Let's first tackle the relationship between the regular price and the unleaded price. They said that the Regular (R) was 5 cents per liter cheaper than the Unleaded (U). So, . Since the Unleaded is more expensive, that's the one with the price to be reduced by 5 cents so that it will match the cheaper Regular price.

She says that she sold 450 liters of regular. If so, then the total amount of money collected from regular gas is . If there were 320 liters sold of unleaded gas, then the money earned from selling the regular gas is . We need to add the money gained from regular and unleaded to equal the total earnings for both gasoline grades:

<---------- Start here

<---------- Since we knew the relationship between the prices per liter of each type of gas, we did a substitution. Since , we went ahead and substituted U - 0.05 in place of R in the main equation. this way, the equation will only be in 1 variable so that it can be solved.

<----- Distribute

<--------- combined like terms

<---------- Added 22.50 to both sides

<----- The price of unleaded is $0.529 per liter. If the regular was 5 cents cheaper than that, it'd be $0.479 per liter.
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