Question

Bill made a nut mixture that contains 67%

peanuts by mixing together 15 oz. of
mixed nuts that contain 65% peanuts and
10 oz. of a different brand of mixed nuts.
The second brand of mixed nuts contained
what percent peanuts?

Answer 1

The second brand of mixed nuts that Bill used to make his 67% peanut mixture contains 70% peanuts. This was found by setting up and solving an equation using the proportions of peanuts and the weights of each brand's nut mix that were combined.

Step-by-step explanation:

Bill created a nut mixture that is 67% peanuts by combining 15 ounces of a 65% peanut mix with 10 ounces of a second brand. The overall mix resulted in 25 ounces of the combined nut mixture. To solve for the percentage of peanuts in the second brand, we can set up an equation using the weights and percentages of peanuts in each part of the mix.

Let x be the percentage of peanuts in the second brand. The total weight of peanuts from both brands is the weight of the final mixture times its percentage in peanuts:

(15 oz × 65%) + (10 oz × x) = (25 oz × 67%)

By converting the percentages into decimal form and calculating, we reach the equation:

9.75 + 10x = 16.75

Solving for x gives us:

10x = 16.75 - 9.75

10x = 7

x = 0.7

Therefore, the second brand contains 70% peanuts.