Brett made muffins for his grandmother, but he gave his friend Steve 1/8 of the muffins. Then Brett saw Dori and gave her 1/3 of what he had left. Then he saw Shiela and gave her 1/7 of what he had left. By the time he arrived at his grandmothers house there were only 12 muffins.
a. How many muffins did Brett make?
b. How many muffins did he give to each person?
Please explain
Thanks,
Mark
To solve this problem, we can work backward starting with the 12 muffins Brett arrived with at his grandmother's house.
Let's assign the number of muffins Brett initially made as "x".
a. How many muffins did Brett make?
To find the original number of muffins Brett made, we need to reverse the process.
1. Brett gave Steve 1/8 of the muffins he had left.
After giving Steve 1/8 of the muffins, Brett was left with 7/8 of the muffins.
So, 7/8 of x muffins remained.
2. Brett then gave Dori 1/3 of what he had left.
After giving Dori 1/3 of the muffins, Brett was left with 2/3 of the muffins.
So, 2/3 * 7/8 * x muffins remained.
3. Finally, Brett gave Shiela 1/7 of what he had left.
After giving Shiela 1/7 of the muffins, Brett was left with 6/7 of the muffins.
So, 6/7 * 2/3 * 7/8 * x = 12 muffins.
Now, let's solve the equation for x:
6/7 * 2/3 * 7/8 * x = 12
To simplify the equation, cancel out common factors:
2/3 * 1/1 * 1/1 * x = 12
2/3 * x = 12
Multiply both sides by 3/2 to solve for x:
x = (12 * 3) / 2
x = 18
Therefore, Brett initially made 18 muffins.
b. How many muffins did he give to each person?
Now that we know Brett initially made 18 muffins, we can calculate how many muffins he gave to each person using the given fractions.
1. Brett gave Steve 1/8 of the muffins:
18 * (1/8) = 2.25 muffins
Since you cannot have a fraction of a muffin, Brett gave Steve 2 muffins.
2. Brett then gave Dori 1/3 of what he had left:
(18 - 2) * (1/3) = 4 muffins
3. Finally, Brett gave Shiela 1/7 of what he had left:
(18 - 2 - 4) * (1/7) = 2 muffins
Therefore, Brett gave Steve 2 muffins, Dori 4 muffins, and Shiela 2 muffins.
X - 1/8X - (1/3 * 7/8)X - (1/3 * 7/8 * 1/7)X = 12
Solve for X to get total. Multiply by the indicated fractions to get the muffins given to each person.
I hope this helps. Thanks for asking.