Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash a car and $15 to wash a truck. In 270 minutes, Evan made $105 washing cars and trucks. How many trucks did Evan wash?
30 c + 40 t = 270 ... 3 c + 4 t = 27
12 c + 15 t = 105
solve the system
12 c + 16 t = 108
To solve this problem, let's use a system of equations.
Let's assume that the number of cars Evan washed is represented by 'c', and the number of trucks Evan washed is represented by 't'.
According to the given information, it takes Evan 30 minutes to wash a car. So, the total time spent washing cars would be 30c minutes.
Similarly, it takes Evan 40 minutes to wash a truck. So, the total time spent washing trucks would be 40t minutes.
We also know that Evan made $12 washing each car and $15 washing each truck. So, the total amount made washing cars would be $12c, and the total amount made washing trucks would be $15t.
Given that Evan made $105 in 270 minutes, we can create two equations based on time and earnings:
Equation 1: 30c + 40t = 270 (since Evan spent 30c minutes washing cars and 40t minutes washing trucks, which totals 270 minutes)
Equation 2: 12c + 15t = 105 (since Evan made $12c washing cars and $15t washing trucks, which totals $105)
Now we can solve these equations simultaneously to find the values of 'c' and 't'.
Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate the coefficients of 'c':
90c + 120t = 810 (Equation 3)
24c + 30t = 210 (Equation 4)
Subtracting Equation 4 from Equation 3:
(90c - 24c) + (120t - 30t) = 810 - 210
66c + 90t = 600 (Equation 5)
Now we have two equations:
66c + 90t = 600 (Equation 5)
12c + 15t = 105 (Equation 2)
We can solve these equations simultaneously using any appropriate method, such as substitution or elimination.
Simplifying Equation 2 by dividing both sides by 3:
4c + 5t = 35 (Equation 6)
Now we have two simplified equations:
66c + 90t = 600 (Equation 5)
4c + 5t = 35 (Equation 6)
Multiplying Equation 6 by 18 to eliminate the coefficients of 'c':
72c + 90t = 630 (Equation 7)
Now we have two simplified equations:
66c + 90t = 600 (Equation 5)
72c + 90t = 630 (Equation 7)
Subtracting Equation 5 from Equation 7:
(72c - 66c) + (90t - 90t) = 630 - 600
6c = 30
Dividing both sides of the equation by 6:
c = 5
So, Evan washed 5 cars.
Now substitute the value of 'c' in Equation 6 to find the value of 't':
4(5) + 5t = 35
20 + 5t = 35
5t = 35 - 20
5t = 15
Dividing both sides of the equation by 5:
t = 3
Therefore, Evan washed 3 trucks.
In conclusion, Evan washed 3 trucks.