Question 143822

Let x=amount of 65% solution needed

Now we know that the amount of pure salt in the 30% solution (0.30*40) plus the amount of pure salt in the 65% solution (0.65x) has to equal the amount of pure salt in the final mixture (0.50(40+x)).  So our equation to solve is:

0.30*40+0.65x=0.50(40+x)  get rid of parens (distributive law)

12+0.65x=20+0.50x  subtract 0.50x and also 12 from each side

12-12+0.65x-0.50x=20-12+0.50x-0.50x  collect like terms

0.15x=8  divide each side by 0.15

x=53 1/3 cups or approximately 53 cups-----------ans


CK

0.30*40+0.65*53=0.50*93

12+34.45=46.5
46.45~~~~~~~~~~~~~~~~~~~46.5

Hope this helps---ptaylor