A baker has a bag of flour that is 11% whole wheat and a bag of flour that is 63% whole wheat. How many cups of each type does the baker need to make 12 cups of a flour mixture that is 50% whole wheat?
a. 3 cups of the 11% flour and 9 cups of the 63% flour***
b. 9 cups of the 11% flour and 3 cups of the 63% flour
c. 3 cups of the 11% flour and 3 cups of the 63% flour
d. 9 cups of the 11% flour and 9 cups of the 63% flour
correct
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To solve this problem, we can use a basic equation:
(0.11x) + (0.63y) = 0.50(12)
Where:
- x represents the number of cups of the 11% flour
- y represents the number of cups of the 63% flour
By solving this equation, we can find the values of x and y. Let's calculate:
0.11x + 0.63y = 6
To make the equation simpler, we can multiply both sides of the equation by 100:
11x + 63y = 600
To continue, we need to use a system of equations. We'll create another equation to represent the total number of cups:
x + y = 12
Now we have a system of equations:
11x + 63y = 600
x + y = 12
To solve this system, we can use the substitution method. Let's solve for x in the second equation:
x = 12 - y
Now substitute this value into the first equation:
11(12 - y) + 63y = 600
132 - 11y + 63y = 600
52y = 468
y = 9
Now we can substitute the value of y back into x = 12 - y:
x = 12 - 9
x = 3
Therefore, the baker needs 3 cups of the 11% flour and 9 cups of the 63% flour to make a 50% whole wheat flour mixture. So, the correct answer is:
a. 3 cups of the 11% flour and 9 cups of the 63% flour
To solve this problem, we can use the concept of the weighted average. Let's break down the problem step by step:
1. Let's assume that the baker needs x cups of the 11% whole wheat flour and y cups of the 63% whole wheat flour to make a mixture of 12 cups that is 50% whole wheat.
2. We can write two equations to represent the given information:
Equation 1: (x cups of 11% flour) + (y cups of 63% flour) = 12 cups (total mixture)
Equation 2: [(11% whole wheat content * x cups of 11% flour) + (63% whole wheat content * y cups of 63% flour)] / (x cups + y cups) = 50% whole wheat content
3. Simplify Equation 2:
(0.11x + 0.63y) / (x + y) = 0.50
4. Cross-multiply to eliminate the fraction:
0.11x + 0.63y = 0.50(x + y)
0.11x + 0.63y = 0.50x + 0.50y
5. Rearrange the equation:
0.13x = 0.13y
x = y
6. From Equation 1, we know that x + y = 12. Since x and y are equal, we can rewrite the equation as:
2x = 12
x = 6
y = 6
7. Therefore, the baker needs 6 cups of the 11% flour and 6 cups of the 63% flour.
Thus, the correct answer is option c: 3 cups of the 11% flour and 3 cups of the 63% flour.