Question

Brand A granola is 25% nuts and dried fruit and brand B granola is 20% nuts and dried fruit. How much of sweet item A and sweet item B should be mixed to form a 20 lb batch of sweets that is 23% nuts and dried fruit

Answer 1

Brand A = 25% nuts & dried fruit

Brand B = 20% nuts and dried fruit

we want to mix then so as to get a 20 lb batch of 23% nuts an dried fruit.

So we create 2 equations, naming A the amount of Brand A granola, and B the amount (in pounds) of Brand B granola.

then the first equation (the easiest one):

A + B = 20 (since the addition of both should give 20 pounds)

second equation should be based on the amount of nuts and dried fruit that each brand provides to the mix:

recall that 25% in math form is written as: 0.25, 23 % is written as 0.23,

and 20% as 0.20

0.25 A + 0.20 B = 0.23 (20)

because the amount of nuts and dried fruit in the oart from Brand A plust the same for the part from brand B, should give the amount of numts and dried fruit in the 20 pounds of the final mix.

Now, we solve for B for example in the first equation we wrote:

B = 20 - A

and use "substitution" of this variable in the second equation:

0.25 A + 0.20 (20 - A) = 0.23 (20)

0.25 A - 0.20 A + 4 = 4.6

0.05 A = 4.6 - 4

0.05 A = 0.6

A = 0.6 / 0.05

A = 12 pounds

Then if A is 12 pounds, then brand B granola should be:

B = 20 - 12 = 8 pounds

Finals andswer:

We need 12 pounds of brand A, and 8 pounds of brand B.