a dealer has 30 cars and trucks. If 2 more cars are delivered, the dealer will have 3 times as many cars as trucks. How many trucks does the dealer presently have?
t + 3t = 32
Solve for t.
Step 1:
Define variables:
c=number of cars
t=number of trucks
"a dealer has 30 cars and trucks" translates to
c+t=30
which means
t=30-c .....(1)
"If 2 more cars are delivered, the dealer will have 3 times as many cars as trucks." translates to
c+2=3t .....(2)
Substitute (1) in (2)
c+2 = 3(30-c) .....(3)
Solve for c:
4c=88, or c=22, so t=30-c=8
Answer: there are 22 cars and 8 trucks.
To find out how many trucks the dealer presently has, we can use algebraic equations to solve the problem. Let's assume the number of trucks is "t."
According to the given information, the dealer presently has 30 cars and trucks combined. We can represent this information as:
Number of trucks (t) + Number of cars = Total number of cars and trucks
t + 30 - t = 30
Simplifying the equation, we find that:
30 = 30
This equation tells us that the total number of cars and trucks is currently 30.
Now, the problem states that if 2 more cars are delivered, the dealer will have three times as many cars as trucks. We can represent this information as:
Number of trucks (t) = Number of cars (3t) - 2
Substituting 3t - 2 for the number of cars, we have:
t + 3t - 2 = 30
Combining the terms, we simplify the equation to:
4t - 2 = 30
Adding 2 to both sides of the equation, we get:
4t = 32
Dividing both sides of the equation by 4, we find:
t = 8
Therefore, the dealer presently has 8 trucks.