In a cookie shop, 3/4 of the cookies baked were chocolate cookies and the rest were strawberry cookies. After 222 chocolate cookies and 2/5 of the strawberry cookies were sold, the number of strawberry cookies left were 1/3 the number of chocolate cookies left.
(a) How many more chocolate cookies than strawberry cookies were sold?
(b) How many cookies were baked at first?
If there were x cookies to start with, then
3/4 x - 222 = 3(1/4 x - (2/5)(1/4 x))
(b) x = 740 cookies in all were baked
Now you can answer (a)
To solve this problem, let's break it down step by step.
Step 1: Determine the number of chocolate and strawberry cookies left
In the cookie shop, 3/4 of the cookies were chocolate cookies and the rest were strawberry cookies. Let's assume the total number of cookies baked was C.
Number of chocolate cookies baked = 3/4 of C
Number of strawberry cookies baked = 1/4 of C
Now, let's calculate the number of chocolate cookies and strawberry cookies left after some were sold.
Number of chocolate cookies left = (3/4 * C) - 222
Number of strawberry cookies left = (1/4 * C) - (2/5 * 1/4 * C) [Since 2/5 of the strawberry cookies were sold]
Step 2: Determine the relationship between the number of chocolate and strawberry cookies left
According to the problem, the number of strawberry cookies left is 1/3 the number of chocolate cookies left.
So, we can set up the following equation:
Number of strawberry cookies left = 1/3 * Number of chocolate cookies left
Step 3: Solve the equation
Now, let's substitute the expressions for the number of chocolate and strawberry cookies left into the equation:
(1/4 * C) - (2/5 * 1/4 * C) = 1/3 * [(3/4 * C) - 222]
Simplifying this equation will give us the value for C, the total number of cookies baked.
After finding the value for C, we can calculate the number of cookies of each type sold (difference between the baked and remaining) to answer question (a), and the total number of cookies baked to answer question (b).