SOLUTION: How many lb. of metal containing 70% gold must be combined with 9 lb. of metal containing 5% gold to form an alloy containing 25% gold?
Algebra ->
College
-> Linear Algebra
-> SOLUTION: How many lb. of metal containing 70% gold must be combined with 9 lb. of metal containing 5% gold to form an alloy containing 25% gold?
Log On
Question 1090318: How many lb. of metal containing 70% gold must be combined with 9 lb. of metal containing 5% gold to form an alloy containing 25% gold? Answer by ikleyn(52781) (Show Source):
Classic/standard mixture problem for alloys, and standard solution.
Let x be an amount (in lb) of the metal containing 70% gold to be combined.
Then 0.7x is the gold content in this metal (in lb),
while 0.05*9 is the gold content in the other, 5% metal.
The gold balance equation is
0.7x + 0.05*9 = 0.25(x+9).
Multiply both sides by 100 to make things easier. You will get
70x + 5*9 = 25(x+9).
Simplify and solve for x.
70x + 45 = 25x + 225 ====> 70x - 25x = 225 - 45 ====> 45x = 180 ====> x = = 4.
Answer. 4 pounds of the metal containing 70% of gold is needed.
