According to a rating agency, a car's MPG (miles per gallon) ratings are: 25 MPG for city and 30 MPG for highway driving. A driver spent $20.00 (the gasoline costs $1.25/gallon) on a combined city and highway trip of 450 miles. How many miles "C" in city and "H" on highway was the car driven ?
I need to put this into 2 equations. How does the $20.00 fit into the equation?
<<How does the $20.00 fit into the equation? >>
Let C = city miles and H = highway miles
City gas cost + Highway gas cost = $20
(C/25)*1.25 + (H/30)*1.25 + 20
0.05 C + 0.04167 H = 20
Combine that with
C + H = 450
to get the answer.
C + 0.8333 H = 400
.16667 H = 50
H = 300 miles
C = 150 miles
To solve this problem, let's first define two variables: "C" for the number of miles driven in the city and "H" for the number of miles driven on the highway.
Since we know that the MPG rating for city driving is 25 and for highway driving is 30, we can set up the following equations:
1. The total number of miles driven equals the sum of the miles driven in the city and on the highway:
C + H = 450
2. The total cost of gasoline used on the trip equals the cost per gallon multiplied by the total number of gallons used. We can calculate the total gallons used by dividing the number of miles driven by the MPG:
($1.25/gallon) * (C/25 + H/30) = $20.00
In the second equation, we divided the miles driven in the city (C) by the city MPG (25), and the miles driven on the highway (H) by the highway MPG (30). This gives us the total gallons used in both city and highway driving.
Now we have two equations: C + H = 450 and ($1.25/gallon) * (C/25 + H/30) = $20.00. We can solve this system of equations to find the values of C and H.