Question

PLEASE HELP

1.How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?

2.A chemist needs to mix a 12% acid solution with a 32% acid solution to
obtain an 8‐liters mixture consisting of 20% acid. How many liters of each of
the acid solutions must be used?

Answer 1

9514 1404 393

Answer:

1. 10
2. 12%: 4.8 L; 32%: 3.2 L

Explanation:

For mixture problems, I like to use a single variable to represent the quantity of the greatest contributor (greatest cost or greatest concentration). Let that variable be x.

1. In this problem, the amount of the greatest contributor is already fixed, so we'll use x for the amount of walnuts. The cost of the mix is ...

0.80x + 1.25(8) = 1.00(x +8)

2 = 0.2x . . . . . . . . . . . . . . . . . subtract 0.8x+8, simplify

10 = x . . . . . . . . . divide by 0.2

10 pounds of walnuts must be used.

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2. The amount of acid in the mix is ...

12%(8 -x) +32%(x) = 20%(8)

20%(x) = 8%(8) . . . . . . . . . . . . subtract 12%(8)

x = 8(8)/20 = 3.2 . . . . . . . . . . divide by 20%

8-x = 4.8

3.2 liters of 32% acid must be mixed with 4.8 liters of 12% acid

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Comment on mixture problems

The general solution for mixture problems that have a greater contributor (G), a lesser contributor (L), and a mix value (M) is ...

g/l = (M -L)/(G -M) . . . . . . ratio of quantities of G and L

In the first problem, this becomes ...

8/l = (1.00 -.80)/(1.25 -1.00) = .2/.25 = 4/5 ⇒ l = 8(5/4) = 10

In the second problem, this becomes ...

g/l = (20-12)/(32-20) = 8/12 = 2/3 ⇒ g = (2/5)(8) = 3.2; l = (3/5)(8) = 4.8

In this case, we recognize that the ratio of 2 parts to 3 parts means that the greater contributor is 2 of 5 total parts.