Question

A bread company likes to mix 40% whole wheat flour and 70% whole wheat flour to get 60% whole wheat flour. If they need 45 kilograms of 60% whole wheat flour, how much of each type of flour should be used?

Answer 1

The company should mix 15 kilograms of 40% whole wheat flour with 30 kilograms of 70% whole wheat flour to achieve 45 kilograms of 60% whole wheat flour.

Step-by-step explanation:

The question involves a mixture problem where a bread company wants to combine two types of whole wheat flour to achieve a desired percentage of whole wheat in their flour mix. They need to produce 45 kilograms of 60% whole wheat flour using 40% and 70% whole wheat flour blends. To solve this problem, we'll use the method of weighted averages.

1. Let the amount of 40% whole wheat flour needed be x kilograms.
2. The amount of 70% whole wheat flour needed would then be (45 - x) kilograms.
3. Set up the equation using the weighted average: (0.40x) + (0.70(45 - x)) = 0.60(45).
4. Solve the equation for x to find the kilograms of the 40% flour.
5. Subtract x from 45 to get the kilograms of the 70% flour.

Upon solving:

• 0.40x + 31.5 - 0.70x = 27
• -0.30x = -4.5
• x = 15

The bread company should use 15 kilograms of 40% whole wheat flour and 30 kilograms of 70% whole wheat flour.

Answer 2

The bread company needs 15 kilograms of 40% whole wheat flour and 30 kilograms of 70% whole wheat flour to create 45 kilograms of 60% whole wheat flour.

Step-by-step explanation:

To solve for the amount of each type of flour required to achieve 45 kilograms of 60% whole wheat flour, we can set up a system of equations based on the percentages of whole wheat in each type of flour and the total mixture required.

Let x represent the amount of 40% whole wheat flour and y represent the amount of 70% whole wheat flour. We can set up the following equations:

• x + y = 45 (total weight of the mixture)
• 0.40x + 0.70y = 0.60 × 45 (total percentage of whole wheat in the mixture)

Solving the system of equations, we find:

1. 0.40x + 0.70y = 27 (equation 2 simplified)
2. Multiply equation 1 by 0.40, we get 0.40x + 0.40y = 18
3. Subtract the modified equation 1 from equation 2:
   1. 0.70y - 0.40y = 27 - 18
   2. 0.30y = 9
   3. y = 9/0.30
   4. y = 30
4. Substituting y = 30 into equation 1:
   1. x + 30 = 45
   2. x = 45 - 30
   3. x = 15

Therefore, the bread company needs 15 kilograms of 40% whole wheat flour and 30 kilograms of 70% whole wheat flour to make 45 kilograms of 60% whole wheat flour.