A family has two cars. The first car has a fuel efficiency of
30
miles per gallon of gas and the second has a fuel efficiency of
25
miles per gallon of gas. During one particular week, the two cars went a combined total of
1275
miles, for a total gas consumption of
45
gallons. How many gallons were consumed by each of the two cars that week?
car x = 30 mpg
car y = 25 mpg
x = 45 - y
30x + 25y = 1275
30(45-y) + 25y = 1275
Solve for y, then x.
Got it. Thank you
Welcome
can you do the same question but with a combined total of 1250 miles
Well, let's go ahead and solve this problem one gallon at a time.
If we let x be the number of gallons consumed by the first car, then we can say that the number of gallons consumed by the second car is (45 - x) gallons.
Now, let's convert the fuel efficiency of the first car into miles per gallon per car:
30 miles per gallon / 1 car = 30 miles per (x) gallons
x gallons * 30 miles per gallon = 30x miles
Similarly, for the second car, we have:
25 miles per gallon / 1 car = 25 miles per (45 - x) gallons
(45 - x) gallons * 25 miles per gallon = 25(45 - x) miles
Now, since the combined total is 1275 miles, we can set up the equation:
30x + 25(45 - x) = 1275
Now, we just need to solve for x, the number of gallons consumed by the first car.
30x + 1125 - 25x = 1275
5x = 150
x = 30
So, the number of gallons consumed by the first car is 30 gallons, and the number of gallons consumed by the second car is 45 - 30 = 15 gallons.
Therefore, the first car consumed 30 gallons and the second car consumed 15 gallons.
To find out how many gallons were consumed by each car, we can set up a system of equations.
Let's say the number of gallons consumed by the first car is x, and the number of gallons consumed by the second car is y.
According to the problem, the combined total of miles driven by both cars is 1275 miles. So we can write the equation:
x + y = 1275 ...........(1)
We also know that the fuel efficiency of the first car is 30 miles per gallon, and the fuel efficiency of the second car is 25 miles per gallon. This means that the number of gallons consumed by each car can be calculated by dividing the total number of miles driven by their respective fuel efficiency. So we can write equations for this as well:
x/30 = y/25 ...........(2)
Now we have a system of two equations (equations 1 and 2) with two unknowns (x and y). We can solve this system to find the values of x and y, which will give us the number of gallons consumed by each car.
To solve this system, let's use the method of substitution:
Step 1: Solve equation 2 for x in terms of y:
x = (30/25)y
Step 2: Substitute this expression for x in equation 1:
(30/25)y + y = 1275
Simplify the equation by combining like terms:
(30/25 + 1)y = 1275
Combine the fractions:
(55/25)y = 1275
Multiply both sides by (25/55) to isolate y:
y = (1275 * 25) / 55
Simplify the expression:
y = 575
Step 3: Substitute the value of y back into equation 1 to find x:
x + 575 = 1275
Subtract 575 from both sides:
x = 1275 - 575
Simplify the expression:
x = 700
So, the first car consumed 700 gallons and the second car consumed 575 gallons during that week.