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?

A detailed explaination of how to get the answer would be greatly appreciated thanks!

  • $\begingroup$ Welcome to MathSE! We prefer if you add some more details to your question: what have you tried and where do you get stuck? This will help other users give good answers. $\endgroup$ – Johanna Mar 21 '15 at 15:11
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    $\begingroup$ Hello. Well I have no idea where to begin in this problem, I know there is an equation here somewhere but I can't identify it correctly. So far I tried [21(.29)= (.35)A + (.25)B] but that doesn't help at all because there's still 2 variables. I just simply want to know how to properly arrive at the answer, thanks. $\endgroup$ – Ambrose Mar 21 '15 at 15:18

As noted in a comment, you had already found that

$$(0.29)21= (0.35)A + (0.25)B.$$

The interpretation of this is that $A$ is the amount of mixed nuts of Brand A that are used, and $B$ is the amount of mixed nuts of Brand B. The left side indicates that the mixture contains $21$ ounces of nuts.

To be extra clear, I'll repeat the preceding paragraph in slightly different words:

The manufacturer takes $A$ ounces of one brand of nuts and $B$ ounces of another brand of nuts to make $21$ ounces of mixed nuts.

Using just the information in the previous paragraph, you can write another equation involving $A$ and $B$. The numbers $0.29$, $0.35$, and $0.25$ were not mentioned in that paragraph, so they do not occur in the equation.

You will then have a sufficient mathematical model to solve the problem.


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