Question 111614

Let x=amount of 3/4 pure gold needed

Then 6-x=amount of 5/12 pure gold needed

Now we know that the amount of pure gold in the 3/4 alloy ((3/4)x) plus the amount of pure gold in the 5/12 alloy ((5/12)(6-x)) has to equal the amount of pure gold in the final alloy(6*(2/3)).  So our equation to solve is:

(3/4)x+(5/12)(6-x)=6*(2/3)  simplify

(3/4)x+(5/2)-(5/12)x=4  multiply each term by 12 (LCM)

9x+30-5x=48  subtract 30 from both sides
9x-5x+30-30=48-30  collect like terms

4x=18  divide both sides by 4

x=4.5 oz----------------------amount of 3/4 pure gold needed

6-x=6-4.5=1.5 oz-----------------------amount of 5/12 pure gold needed

CK

(4.5)(3/4)+(1.5)(5/12)=6(2/3)

3.375+0.625=4
4=4

Hope this helps---ptaylor