Question

How many ounces of peanuts must Krystal add to 20 ounces of mixed nuts containing 40% peanuts to make a mixture with 50% peanuts?

A) 2 ounces
B) 4 ounces
C) 5 ounces
D) 10 ounces

Answer 1

Krystal must add 4 ounces of peanuts to the 20 ounces of mixed nuts in order to create a mixture that is 50% peanuts.

Step-by-step explanation:

To find out how many ounces of peanuts Krystal must add to 20 ounces of mixed nuts containing 40% peanuts to make a mixture with 50% peanuts, we can set up an equation based on the weight of the peanuts in each portion of the mixture.

Initially, there are 20 ounces of mixed nuts with 40% peanuts. This means there are 20 ounces x 40% = 8 ounces of peanuts in the mixture.

Let x be the number of ounces of peanuts that Krystal adds to the mixture. The total weight of the mixture after adding the peanuts will be (20 + x) ounces, and the amount of peanuts will be (8 + x) ounces.

We want the final mixture to be 50% peanuts, so we set up the following equation representing this condition:

50% x (20 + x) = (8 + x)

Dividing both sides of the equation by 50% (or 0.5) gives:

(20 + x) = 2 * (8 + x)

Simplifying, we get:

20 + x = 16 + 2x

x = 4 ounces

So, Krystal must add 4 ounces of peanuts to the mixture to have a final mixture with 50% peanuts.