Question

brand A granola is 25% nuts and dried fruit and brand B granola is 10% nuts and dried fruit. how much of sweet item A and sweet item B should be mixed to form a 20lb batch of sweets that is 13%nuts and dried fruit?

Answer 1

Let A represent brand A, and B represent brand B. This implies that

`\begin{gathered} A\Rightarrow brand\text{ A} \\ B\Rightarrow brand\text{ B} \end{gathered}`

Given that A is 25% nuts and dried fruit, and B is 10% nuts and dried fruit, this implies that the total mixture is expressed as

`Total\text{ mixture = }25A+20B`

If A and B are mixed to form a 20 lb batch of sweet that is 13% nuts and dried fruit, thus implies that

`\begin{gathered} Total\text{ mixture = 13\lparen20\rparen=260} \\ thus, \\ 25A+20B=260\text{ ----- equation 1} \end{gathered}`

Also, given that A and B are mixed to form 20 lb batch, this implies that

`A+B=20\text{ ----- equation 2}`

To solve the amount of A and B, we solve the equations simultaneously.

Step 1: From equation 2, make B the subject of the equation.

Thus,