Finding percent

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is
40%
salt and Solution B is
65%
salt. She wants to obtain
170
ounces of a mixture that is
55%
salt. How many ounces of each solution should she use?

Answer 1

 x=# of ounces of the 40% solution

170-x=# of ounces of the 65% solution

40%x+65%(170-x)=55%(170)

0.4x+0.65(170-x)=0.55(170)

0.4x+110.5-0.65x=93.5

-0.25x=-110.5+93.5

-0.25x=-17

0.25x=17

25x=1700

x=1700/25

x=68 ounces of the 40% solution

170-68=102 ounces of the 65% solution

 

Answer 2

I used trial and error to come up with the percentages. There may be an easier way to determine the percentage to use of each solution. I started with 50% of each solution. So we have 40%(50%) + 65%(50%) = 52.5% or .4(.5) + .65(.5) = .525 Since the value was less than 55%, we have to increase our result. To do this, decrease the amount of 40% solution and increase the amount of 65% solution. So we have 40%(40%) + 65%(60%) = 55% or .4(.4) + .65(.6) = .55  Then, to determine the amount of each, do 170(.4) = 68 ounces for solution A, and 170(.6) = 102 ounces for solution B.