Solve the following question Brand X sells 21 oz bags of mix

Solve the following 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?

Please give a full explanation and show all work. No handwritten work.

Solution

Let x = Oz of brand A nuts and y = Oz of brand B nuts. Then from the given information,

x + y = 21 ... (1) and

0.35x + 0.25 b = 0.29 (21)

This gives

0.35x + 0.25 b = 6.09 ...(2)

Now multiply both sides of (1) by 0.35,

0.35 x + 0.35 y = 7.35 .... (3)

Subtract (2) from (3),

0.1 y = 1.26

y = 1.26/0.1 = 12.6 Oz

Substituting this in (1),

x + 12.6 = 21

x= 21 - 12.6 = 8.4 Oz

So the answer is

x= 8.4 Oz and y=12.6 Oz