Adrianne is planning to bake some chocolate, strawberry, and raisin muffins for a party. She was asked to bake half as many chocolate muffins as raisin muffins and three times as many strawberry muffins as chocolate muffins. If she only had enough ingredients to bake 480 muffins, how many raisin muffins did she bake?
c = 1/2 r
s = 3c
c+r+s = 480
Now just solve for r
To solve this problem, let's start by assigning variables to the number of each type of muffin that Adrianne bakes.
Let:
x = number of chocolate muffins
y = number of strawberry muffins
z = number of raisin muffins
According to the information given in the problem, the following conditions are met:
1. Adrianne bakes half as many chocolate muffins as raisin muffins.
This can be represented as: x = (1/2)z
2. Adrianne bakes three times as many strawberry muffins as chocolate muffins.
This can be represented as: y = 3x
3. Adrianne bakes a total of 480 muffins.
This can be represented as: x + y + z = 480
Now we can use this information to solve the system of equations.
1. Substitute the value of x from equation 1 into equation 2:
y = 3((1/2)z)
y = (3/2)z
2. Substitute the values of x and y into equation 3:
((1/2)z) + (3/2)z + z = 480
(1/2z + 3/2z + z) = 480
(6/2)z = 480
3z = 480
z = 160
Therefore, Adrianne baked 160 raisin muffins.
Let's denote the number of raisin muffins as 'x.'
According to the given information, Adrianne is planning to bake half as many chocolate muffins as raisin muffins. So, the number of chocolate muffins is (1/2)x.
Also, she plans to bake three times as many strawberry muffins as chocolate muffins. So, the number of strawberry muffins is 3 * (1/2)x = (3/2)x.
The total number of muffins is the sum of chocolate, strawberry, and raisin muffins, which is:
(1/2)x + (3/2)x + x = 480
Combining similar terms:
(2/2)x + (3/2)x + x = 480
(6/2)x = 480
3x = 480
Divide both sides of the equation by 3:
3x/3 = 480/3
x = 160
Therefore, Adrianne baked 160 raisin muffins.