In one month a salesman sold a total of 30 cars and trucks. If three times the number of cars sold equals twice the number of trucks sold, how many trucks did he sell?
Let's start by assuming the number of cars sold as "x" and the number of trucks sold as "y".
According to the information given, the salesman sold a total of 30 cars and trucks. So, we can write the equation:
x + y = 30 (Equation 1)
It is also mentioned that three times the number of cars sold equals twice the number of trucks sold. We can write the equation:
3x = 2y (Equation 2)
Now, we can solve the system of equations (Equation 1 and Equation 2) to find the values of x and y.
Multiplying Equation 2 by 3, we get:
9x = 6y
Rearranging the equation:
6y = 9x
Dividing both sides by 6:
y = (9/6)x
Now, substitute the value of "y" in Equation 1:
x + (9/6)x = 30
Combining like terms:
(15/6)x = 30
To get rid of the fraction, multiply both sides by 6/15:
x = 30 * (6/15)
Simplifying:
x = 12
Substitute the value of "x" in Equation 1:
12 + y = 30
Subtracting 12 from both sides:
y = 30 - 12
Simplifying:
y = 18
Therefore, the salesman sold 18 trucks.
To find the number of trucks the salesman sold, we can set up a system of equations based on the given information.
Let's assume the number of cars sold is represented by "C" and the number of trucks sold is represented by "T".
From the problem, we know that the salesman sold a total of 30 cars and trucks. Therefore, we can write the equation:
C + T = 30 ---(equation 1)
We are also given that three times the number of cars sold equals twice the number of trucks sold:
3C = 2T ---(equation 2)
Now that we have a system of equations, we can solve it to find the number of trucks sold.
We can solve the system using substitution or elimination. Let's solve it using substitution method:
- Solve equation 2 for C:
C = (2/3)T
- Substitute this value of C in equation 1:
(2/3)T + T = 30
- Simplify the equation:
(2T + 3T)/3 = 30
(5T/3) = 30
- Multiply both sides of the equation by 3 to eliminate the fraction:
5T = 90
- Divide both sides of the equation by 5 to solve for T:
T = 18
Therefore, the salesman sold 18 trucks.
c+t=30
3c = 2t