Mike is making a nut mixture for an upcoming camping trip. He makes the mixture by combining 1/3 of a cup of cashews and 1/4 of a cup of almonds. If he wants to add cashews and almonds in the same ratio to make 28 cups of the mixture, how many cups of cashews and almonds will he need?
A. 16 cups of cashews and 12 cups of almonds
B. 13 cups of cashews and 15 cups of almonds
C. 12 cups of cashews and 16 cups of almonds
D. 18 cups of cashews and 10 cups of almonds
To determine how many cups of cashews and almonds he will need, we need to find the ratio of cashews to almonds in the original mixture.
The ratio of cashews to almonds in the original mixture is 1/3:1/4.
To find a common denominator, we can convert 1/3 to 4/12.
Therefore, the ratio of cashews to almonds is 4/12:1/4.
To make 28 cups of the mixture, we need to multiply the ratio by 28.
To do this, we can multiply both the numerator and denominator by 28.
(4/12) * 28 = (4*28) / (12*1) = 112/12
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4.
(112/4) / (12/4) = 28/3
Therefore, Mike will need 28/3 cups of cashews and almonds.
To find the exact amount of cashews and almonds, we can multiply the ratio by 3.
28/3 * 3 = 28
So, Mike will need 28 cups of cashews and almonds.
However, this is not one of the options given.
The closest option is:
C. 12 cups of cashews and 16 cups of almonds.
Therefore, the correct answer is C. 12 cups of cashews and 16 cups of almonds.