How many ounces of nuts costing 80 cents a pound must be mixed with nu

Question

How many ounces of nuts costing 80 cents a pound must be mixed with nuts costing 60 cents a pound to make a 10-ounce mixture costing 70 cents a pound?
1 pound = 16 ounces

(A) 3 
(B) 4 
(C) 5 
(D) 7 
(E) 8

Source:   Nova GMAT  
Difficulty Level:   600

Luckisnoexcuse · Answer

Ratio. would be 1:1 since 80-70 = 70-60 hence 5 ounce is the answer

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generis · Answer

1. Find proportion of A to B in final mixture.

Let A = nuts costing 80 cents a pound

Let B = nuts costing 60 cents a pound

2. Equation is

(.80)A + (.60)B = .70 (A + B)

==> .8A + .6B = .7A + .7B

3. Isolate each variable on its own side:

.1A = .1B, so

A = B

4. We also know that A + B = 10.

Substitute B = A in that equation:

A + A = 10, hence

2A = 10, and

A = 5

Answer C

In this approach, the conversion information about 1 pound = 16 ounces isn't necessary.
We need the ratio of A to B. 
All quantities are in price per pound. 
The ratio of A to B holds for 10 ounces or 16 ounces. If not convinced:

Let A = volume of nuts costing 80¢/lb = 80¢/16oz
A cost=  \frac{80c}{16}

Let B = volume of nuts costing 60¢/lb = 60¢/16oz
B cost =  \frac{60c}{16}

(A + B) cost = 70¢/lb = 70¢/16oz=  \frac{70c}{16}

(A + B) volume = 10 ounces

(A cost)(A vol) + (B cost)(B vol) = (A+B Cost)(A+B vol)

\frac{80c}{16}(A)+\frac{60c}{16}(B)=\frac{70c}{16}(A+B) 
-- Multiply all the denominators by 16. Do not insert 10 for (A+B). We need variables on both sides.

80(A)+60(B)=70(A+B) 
 80A+60B=70A+70B 
 10A=10B 
 A=B  and  B=A  Substitute to find A's volume:
 (A+B)=10  =>
 (A+A)=10 
 2A=10 
 A=5  
Answer C

amanvermagmat · Answer

70 lies exactly in the middle of 60 and 80. So we need equal quantities of nuts costing 60 cents a pound and 80 cents a pound.

Since required total quantity is 10 pounds, we need '60 cents a pound' nuts = '70 cents a pound' nuts = 5 pounds each

Hence  C answer

gracie · Answer

let x=ounces of 80¢ nuts
80x+60(10-x)=70*10→
x=5 ounces
C

How many ounces of nuts costing 80 cents a pound must be mixed with nu

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