Cara made some cookies for her math club bake sale. She sold 3/5 of them in the morning and 1/4 of the remaining cookies in the afternoon. If she sold 200 more cookies in the morning than in the afternoon, how many cookies did she make?
To solve this problem, we need to find how many cookies Cara made. Let's break it down step by step.
Let's assume the total number of cookies Cara made is x.
In the morning, she sold 3/5 of her cookies, which means she sold (3/5)x cookies.
The remaining cookies after the morning sale would be (2/5)x since she sold 3/5 and 2/5 is what's left.
In the afternoon, she sold 1/4 of the remaining cookies, which would be (1/4)*(2/5)x = (1/10)x.
Now, we are given that she sold 200 more cookies in the morning than in the afternoon. So we can say:
(3/5)x - (1/10)x = 200
To solve this equation, we need to find a common denominator for the fractions. In this case, the common denominator is 10:
(6/10)x - (1/10)x = 200
Now, we can combine the like terms on the left side of the equation:
(5/10)x = 200
Divide both sides of the equation by 5/10 to isolate x:
x = 200 / (5/10)
x = 200 * (10/5)
x = 400
Therefore, Cara made 400 cookies.
To summarize the steps:
1. Assume the total number of cookies Cara made is x.
2. Calculate the number of cookies sold in the morning: (3/5)x.
3. Calculate the number of remaining cookies: (2/5)x.
4. Calculate the number of cookies sold in the afternoon: (1/4) * (2/5)x.
5. Create an equation from the given information: (3/5)x - (1/10)x = 200.
6. Solve the equation: x = 200 / (5/10).
7. Simplify and solve for x: x = 400.
Therefore, Cara made 400 cookies.