Carly and Kyle decided to count the number of red, blue, and yellow cars that they saw. They counted twice as many red cars as blue cars. The number of yellow cars they counted was one third of the number of red cars if they counted a tote of 33 cars. How many of each car did they count?
We have tried three different approaches and have yet to get the answer..
blue cars --- x
red cars ---- 2x
yellows ----- (1/3)2x = 2x/3
x+2x+2x/3 = 33
times 3
3x+6x+2x=99
take over
Let's follow a step-by-step approach to solve this problem.
Let's assume the number of blue cars that Carly and Kyle counted is represented by "x". According to the problem statement, they counted twice as many red cars as blue cars. So, the number of red cars they counted would be 2x.
The problem also states that the number of yellow cars they counted was one-third of the number of red cars. So, the number of yellow cars they counted would be (1/3)*(2x), which simplifies to (2/3)x.
Now, we are given that the total number of cars they counted was 33. So, we can set up the following equation:
x + 2x + (2/3)x = 33
To solve this equation, we can combine the terms on the left-hand side:
(1 + 2 + 2/3)x = 33
Simplifying further:
(7/3)x = 33
Now, we can solve for x by multiplying both sides of the equation by 3/7:
x = (33 * 3/7)
Calculating this, we get:
x = 99/7
This gives us the number of blue cars they counted, but we need a whole number as the answer. So, let's consider the next closest whole number, which is 14.
Therefore, the number of blue cars they counted is 14.
Using this information, we can calculate the number of red cars:
2x = 2 * 14 = 28
And the number of yellow cars:
(2/3)x = (2/3) * 14 = 28/3 (or approximately 9.33)
Since the number of cars should be a whole number, let's consider the next closest whole number, which is 9.
Therefore, the number of yellow cars they counted is 9.
To summarize, Carly and Kyle counted 14 blue cars, 28 red cars, and 9 yellow cars.