SOLUTION: Please help me set this problem up so I can solve it. How many grams of pure gold must be added to 65% alloy of gold to produce 70 grams of 48% alloy?

Question 161154: Please help me set this problem up so I can solve it. How many grams of pure gold must be added to 65% alloy of gold to produce 70 grams of 48% alloy?
Answer by KnightOwlTutor(293) (Show Source): You can put this solution on YOUR website!
This problem is incorrectly written you cannot add a higher percentage of alloy to a pure metal in order to generate a lower % of alloy. The way this problem is written you would have an alloy composition greater than 65% and less than %100.
I think that the equation was supposed to be using 48% alloy and pure gold to make 65% alloy.
First we would convert the percentages to decimal
100%=100/100=1
48%=48/100=.48
65%=65/100=.65
X=# of grams of pure gold
70-x=# of grams of 48% gold alloy
The equation is as follows
1x+.48(70-x)=.65(70)
Use the distributive property
x+33.6-.48x=45.5
add (1-.48)x=.52x

.52x+33.6=45.5
Subtract 33.6 from both sides
.52x=11.9
Divide both sides by .52
x=22.8 grams of pure gold
Let's check
22.8+[47.11(.48)]=45.5
22.8+22.61=45.5
Both sides =
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