Question

An alloy needs to contain between $46\%$ copper and $50\%$ copper. Find the least and greatest
amounts of a $60\%$ copper alloy that should be mixed with a $40\%$ copper alloy in order to end up with thirty pounds of an alloy containing an allowable percentage of copper.

• A. I will need to use between $10$ and $16$ pounds of the $60\%$ alloy.
• B. I will need to use between $11$ and $15$ pounds of the $60\%$ alloy.
• C. I will need to use between $9$ and $15$ pounds of the $60\%$ alloy.
• D. None of these

Answer 1

The correct option is C I will need to use between $9$ and $15$ pounds of the $60\%$ alloy.

Let x = amount of $60$% copper alloy
then
$30-x$ = amount of $40$% copper alloy
Considering least amount:
$0.60x+0.40(30-x)=0.46(30$)
$0.60x+12-0.40x=13.8$
$0.20x+12=13.8$
$0.20x=1.8$
$x=9$ pounds
Considering greatest amount:
$0.60x+0.40(30-x)=0.50\left(30\right)$
$0.60x+12-0.40x=15$
$0.20x+12=15$
$0.20x=3$
$x=15$ pounds