Question

A company sells a container of mixed nuts that is 12% peanuts and another container that is

60% peanuts. How many cups of each mixture would be needed to make 12 cups that is 40% peanuts?
A. 4 cups of the 12% peanuts and 8 cups of the 60% peanuts
B. 8 cups of the 12% peanuts and 4 cups of the 60% peanuts
C. 5 cups of the 12% peanuts and 7 cups of the 60% peanuts
D. 3 cups of the 12% peanuts and 9 cups of the 60% peanuts

Answer 1

To make 12 cups that is 40% peanuts, 5 cups of the 12% peanuts mixture and 7 cups of the 60% peanuts mixture are needed.

Step-by-step explanation:

To find the number of cups of each mixture needed to make 12 cups that is 40% peanuts, we can set up a system of equations.

1. Let x be the number of cups of the 12% peanuts mixture.
2. Then, (12/100)x is the amount of peanuts in the 12% peanuts mixture.
3. Since the mixture is 12%, we have (12/100)x = 0.12x cups of peanuts.
4. Similarly, (60/100)(12 - x) is the amount of peanuts in the 60% peanuts mixture.
5. Since the mixture is 60%, we have (60/100)(12 - x) = 0.60(12 - x) cups of peanuts.
6. Now, we can set up the equation: 0.12x + 0.60(12 - x) = 0.40(12).
7. Simplifying this equation, we get 0.12x + 7.2 - 0.60x = 4.8.
8. Combining like terms, we have -0.48x = -2.4.
9. Dividing both sides by -0.48, we find that x = 5.

Therefore, 5 cups of the 12% peanuts mixture and 12 - 5 = 7 cups of the 60% peanuts mixture are needed to make 12 cups that is 40% peanuts.