Amy baked some chocolate and vanilla muffins.
She gave away 3/5 of the chocolate muffins and 1/7 of the vanilla muffins. She gave exactly half of the total number of muffins.
In the end, she was left with 24 more chocolate muffins than vanilla muffins. How many chocolate muffins did she bake?
And: 1/5 chocolate muffins = 5/7 vanilla muffins.
5/25 chocolate muffins = 5/7 vanilla muffins
10/25 chocolate muffins - 6/7 vanilla muffins > 24
(5-1) units = 24
25 units = (25x24)/4 = 150
Amy baked 150 chocolate muffins.
Is my answer and working correct?
Yes, your answer and working are correct. Amy baked 150 chocolate muffins.
Your answer is correct, but let's go through the working step by step to confirm it:
1. Let's assume that Amy baked x chocolate muffins and y vanilla muffins.
2. She gave away 3/5 of the chocolate muffins, so she is left with 2/5 of the chocolate muffins, which is equal to (2/5)x.
3. She also gave away 1/7 of the vanilla muffins, so she is left with 6/7 of the vanilla muffins, which is equal to (6/7)y.
4. Amy gave away half of the total number of muffins, which means she is left with (1/2)(x + y) muffins.
5. According to the information given, there were 24 more chocolate muffins than vanilla muffins, so (2/5)x = (6/7)y + 24.
6. We are also given that 1/5 of the chocolate muffins is equal to 5/7 of the vanilla muffins, which means (1/5)x = (5/7)y.
From step 6, we can simplify and multiply both sides of the equation by 5 to get (1/5)x = (5/7)y, which becomes:
x = (25/7)y.
Now let's substitute this value of x in step 5:
(2/5)(25/7)y = (6/7)y + 24.
(50/35)y = (6/7)y + 24.
(10/7)y - (6/7)y = 24.
(4/7)y = 24.
y = (7/4)(24) = 42.
Now substitute this value of y back into x = (25/7)y:
x = (25/7)(42) = 150.
Therefore, Amy baked 150 chocolate muffins, which is the correct answer. Well done!