Question

Brand X sells 21 oz. Bags of mixed nuts that contain 29% peanuts. To make their product they combine brand A mixed nuts which contain 35% peanuts and brand B mixed nuts which contain 25% peanuts. How much of each do they need to use

Answer 1

Brand X has to mix 8.4 oz of brand A mixed nuts which contain 35% peanuts and 12.6 oz of brand B mixed nuts which contain 25%, to obtain 21 oz. Bags of mixed nuts that contain 29% peanuts.

Explanation:

Hi

We define

`B_(A)=1oz @ 35\%`, wich means Brand A has 1 oz containing 35% peanuts.

`B_(B)=1oz @ 25\%`, wich means Brand b has 1 oz containing 25% peanuts.

So we can build an equiation system

(1)
`B_(a)+B_(b)=21`

(2)
`0.35 * B_(a)+0.25 * B_(b)=0.29 * 21`, after fixing it a little

(2)
`0.35B_(a)+0.25B_(b)=6.09`

As we can use any method to solve the system, I used a calculator wich thrown the following results
`B_(a)=8.4 \ oz` and
`B_(b)=12.6 \ oz`.