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 10-lb batch of sweetsthat is 22% nuts and dried fruit?The batch of sweets should contain of Brand A granola and of Brand B granola.

Answer 1

Answer:

The batch of sweet should contain 4 lb of Brand A granola

The batch of sweet should contain 6 lb of Brand B granola

Explanations:

Total amount of sweet items = 10 lb

Let the amount of brand A granola be x

Amount of brand B granola = 10 - x

Amount of nuts and dried fruits in the total sweet items = 22% of 10

Amount of nuts and dried fruits in the total sweet items = 0.22 x 10

Amount of nuts and dried fruits in the total sweet items = 2.2lb

Amount of nuts and dried fruits in brand A granola = 25% of x

Amount of nuts and dried fruits in brand A granola = 0.25x

Amount of nuts and dried fruits in brand B granola = 20% of (10-x)

Amount of nuts and dried fruits in brand B granola = 0.2(10 - x)

Amount of nuts and dried fruits in brand A granola + Amount of nuts and dried fruits in brand B granola = Amount of nuts and dried fruits in the total sweet items

0.25x + 0.2(10 - x) = 2.2

0.25x + 2 - 0.2x = 2.2

Collect like terms

0.25x - 0.2x = 2.2 - 2

0.05x = 0.2

x = 0.2 / 0.05

x = 4 lb

The batch of sweet should contain 4 lb of Brand A granola

Amount of brand B granola = 10 - x

Amount of brand B granola = 10 - 4

Amount of brand B granola = 6 lb

The batch of sweet should contain 6 lb of Brand B granola