A certain parking lot has red, white, and blue cars. The number of red cars is 3 more than the number of white cars, and the number of blue cars is 2 times the number of red cars. What could be the total number of cars in the lot?
19, 20, 21, or 22?
r=w+3
b = 2r
so the total number of cars is w + w+3 + 2(w+3) = 4w+9
21 = 4*3 + 9
Well, let me put on my clown nose and calculate for you.
Let's say the number of white cars is x.
That means the number of red cars is x + 3 (because it's 3 more than the number of white cars).
And the number of blue cars is 2 times the number of red cars, which would be 2(x + 3).
To find the total number of cars, we just need to add the three colors together.
Total = x + (x + 3) + 2(x + 3)
Now we can simplify:
Total = x + x + 3 + 2x + 6
Total = 4x + 9
Since we don't have a specific value for x, we can't determine the exact total number of cars. So unfortunately, I'm just a clown and can't give you a solid answer. But hey, at least we did some math together!
Let's solve this step-by-step.
Let's assume the number of white cars is "x".
According to the information given, the number of red cars is 3 more than the number of white cars, so the number of red cars is "x + 3".
The number of blue cars is 2 times the number of red cars, so the number of blue cars is "2(x + 3)".
The total number of cars in the lot is the sum of the red, white, and blue cars, which is:
x + (x + 3) + 2(x + 3)
Simplifying the equation, we get:
x + x + 3 + 2x + 6
Combining like terms, we have:
4x + 9
Now, let's check the given answer choices: 19, 20, 21, or 22.
Plug in these values for x in the simplified equation and see if any of them give a valid total number of cars.
For x = 2:
4(2) + 9 = 8 + 9 = 17 (not a valid option)
For x = 3:
4(3) + 9 = 12 + 9 = 21 (valid option)
Therefore, the total number of cars in the parking lot could be 21.
To solve this problem, let's use the given information to set up equations and find the possible total number of cars in the parking lot.
Let's denote the number of white cars as "W", the number of red cars as "R", and the number of blue cars as "B".
According to the problem, the number of red cars is 3 more than the number of white cars. Therefore, we can write the equation:
R = W + 3
Also, the number of blue cars is 2 times the number of red cars. We can write this equation as:
B = 2R
Now, we need to find the possible values for the total number of cars in the parking lot, which is the sum of the number of white, red, and blue cars (W + R + B).
To do that, let's substitute the values from the given equations into the equation for the total number of cars:
Total number of cars = W + (W + 3) + 2(W + 3)
Simplifying this equation:
Total number of cars = W + W + 3 + 2W + 6
Total number of cars = 4W + 9
We are looking for potential values of the total number of cars, so let's check the answer choices: 19, 20, 21, and 22.
By plugging in these values into the equation 4W + 9, we can determine if they are possible solutions or not:
For 19:
4W + 9 = 19
4W = 19 - 9
4W = 10
This equation has no integer solution for W, so 19 is not a possible total number of cars.
For 20:
4W + 9 = 20
4W = 20 - 9
4W = 11
Again, this equation has no integer solution for W, so 20 is not a possible total number of cars.
For 21:
4W + 9 = 21
4W = 21 - 9
4W = 12
This equation has an integer solution for W (W = 3), so 21 is a possible total number of cars.
For 22:
4W + 9 = 22
4W = 22 - 9
4W = 13
This equation has no integer solution for W, so 22 is not a possible total number of cars.
Therefore, the only possible total number of cars in the parking lot is 21.