Question

A snack company is creating a new snack mix containing dried fruit, nuts, and pretzels. The dried fruit sells for $8.50 per pound, the nuts sell for $12 per pound, and the pretzels sell for $3 per pound. A one-pound bag of the snack mix will contain a mixture of dried fruit and nuts as well as 2 oz. of pretzels. If the company plans to sell a one-pound bag of snack mix for $9.50, how much dried fruit and nuts should it contain? Write your answer in terms of pounds and round the answers to the nearest thousandth.
A. 0.125 lb of pretzels and 0.482 lb of nuts

B. 0.393 lb of nuts and 0.125 lb of dried fruit

C. 0.482 lb of pretzels and 0.125 lb of nuts

D. 0.482 lb of nuts and 0.393 lb of dried fruit

Answer 1

Answer:

D. 0.482 lb of nuts and 0.393 lb of dried fruits

Step-by-step explanation:

Given :

Cost of nuts = $12/ lb

Cost of dried fruit = $8.50/lb

Cost of Pretzels = $3/lb

Cost of snack mix = $9.50/lb

Amount of pretzels in the snack mix = 2 oz

To find :

Amount of nuts = ?

Amount of dried fruits = ?

Solution:

Let the amount of nuts and dried fruits be x and y lb respectively.

w.k.t, 1 lb = 16 oz

Since, 2 oz of pretzels is present in the snack mix, the total amount of nuts and dried fruits in the snack mix is 16-2=14 oz.

∴ x + y = 14/16  = 0.875                     ---------> a

2 oz of pretzels cost = (3/16) * 2 = 3/8 = $0.375

So, the cost of nuts and dried fruits in the snack mix = 9.50-0.375=$9.125  

∴12 x + 8.5 y = 9.125 -----------> b

Now, solving equations a and b, we have

x = 0.482 , y = 0.393

∴ 0.482 lb of nuts and 0.393 lb of dried fruits are present in 1 lb of the snack mix.

So, the answer is

D. 0.482 lb of nuts and 0.393 lb of dried fruits