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?

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(52784) (Show Source): You can put this solution on YOUR website!
.

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.

Solved.

There is entire bunch of introductory lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys (*)
    - Typical word problems on mixtures from the archive
in this site.

The lesson related to alloys marked by (*).

Read the lessons and become an expert in solution mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".

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