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

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 [leave the volume alone till the end]

(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