SOLUTION: A wholesaler wants to blend coffee containing 35% caffeine with a coffee containing 15% caffeine to produce a 500 pound blend of coffee containing 18% caffeine. How much of each ty
Question 136617: A wholesaler wants to blend coffee containing 35% caffeine with a coffee containing 15% caffeine to produce a 500 pound blend of coffee containing 18% caffeine. How much of each type of coffee is required? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=amount of 35% coffee needed
Then 500-x=amount of 15% coffee needed
Now we know that the amount of pure caffine in the 35% coffee(0.35x) plus the amount of pure caffine in the 15% coffee(0.15(500-x)) has to equal the amount of pure caffine in the final mixture(0.18*500). So our equation to solve is:
0.35x+0.15(500-x)=0.18*500 get rid of parens
0.35x+75-0.15x=90 subtract 75 from each side
0.35x+75-75-0.15x=90-75 collect like terms
0.20x=15 divide both sides by 0.20
x=75 lb amount of 35% coffee needed
500-x=500-75=425 lb---------------------amount of 15% coffee needed
CK
0.35*75+0.15*425=0.18*500
26.25+63.75=90
90=90
Hope this helps---ptaylor
