A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1250 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?
(1st * 25) + (2nd * 30) = 1250
1st + 2nd = 45
solve the system for 1st and 2nd
1st car used X gal.
2nd car used Y gal.
Eq1: x + y = 45
Eq2: 25x + 30y = 1250
Multiply Eq1 by -25 and add the Eqs.:
-25x - 25y = -1125
25x + 30y = 1250
sum: 5y = 125
Y = 25
In Eq1, replace Y with 25 and solve for X.
To find out how many gallons were consumed by each car, we can set up a system of two equations.
Let's assume that the first car consumed x gallons of gas and the second car consumed y gallons of gas.
The fuel efficiency of the first car is given as 25 miles per gallon, so the first car traveled x / 25 miles.
The fuel efficiency of the second car is given as 30 miles per gallon, so the second car traveled y / 30 miles.
According to the information given, the total distance traveled by both cars is 1250 miles, so we have the equation:
x / 25 + y / 30 = 1250. ----(equation 1)
We are also given that the total gas consumption for both cars is 45 gallons, so we have the equation:
x + y = 45. ----(equation 2)
To solve this system of equations, we can use substitution or elimination method.
Let's use substitution method to solve the equations.
From equation 2, we can express x in terms of y as x = 45 - y.
Substituting this value of x into equation 1, we get:
(45 - y) / 25 + y / 30 = 1250.
Now we can simplify this equation and solve for y:
[(45 - y) * 30 + y * 25] / (25 * 30) = 1250.
Multiplying through by 25 * 30, we have:
(30 * (45 - y) + 25y) / 750 = 1250.
Expanding the numerator, we get:
(1350 - 30y + 25y) / 750 = 1250.
Combining like terms, we have:
(1350 - 5y) / 750 = 1250.
Now, multiply both sides of the equation by 750:
1350 - 5y = 1250 * 750.
Simplifying, we have:
1350 - 5y = 937500.
Moving the y term to one side and simplifying, we get:
-5y = 937500 - 1350
-5y = 936150
y = -936150 / -5
y = 187230.
Now, substitute the value of y back into equation 2 to solve for x:
x + 187230 = 45
x = 45 - 187230
x = -187185
However, since we're dealing with gallons of gas, the negative values for x and y are not meaningful in this context. Therefore, we discard the negative values.
So, the number of gallons consumed by the first car is 187185 and by the second car is 187230.
To solve this problem, we can set up a system of equations. Let's use x to represent the number of gallons consumed by the first car and y to represent the number of gallons consumed by the second car.
From the given information, we know:
The fuel efficiency of the first car is 25 miles per gallon, and the total consumption of the first car is x gallons.
The fuel efficiency of the second car is 30 miles per gallon, and the total consumption of the second car is y gallons.
Using this information, we can create the following equations:
Equation 1: x + y = 45 (total gas consumption)
Equation 2: (25 * x) + (30 * y) = 1250 (total distance covered by both cars)
To solve this system of equations, we can use substitution or elimination.
Let's use elimination to solve this system:
Multiply Equation 1 by 25 to eliminate x term:
(25 * x) + (25 * y) = 1125 (Equation 3)
Subtract Equation 3 from Equation 2:
(25 * x) + (30 * y) - ((25 * x) + (25 * y)) = 1250 - 1125
(25 * x) + (30 * y) - (25 * x) - (25 * y) = 1250 - 1125
5y = 125
y = 25
Substitute the value of y into Equation 1:
x + 25 = 45
x = 45 - 25
x = 20
Therefore, the first car consumed 20 gallons of gas, and the second car consumed 25 gallons of gas during that week.