Question 1159823
<br>
(1) A standard formal algebraic solution method....<br>
x ounces of 70% juice, plus (130-x) ounces of 95% juice, equals 75% of 130 ounces of juice:<br>
{{{.70(x)+.95(130-x) = .75(130)}}}<br>
Solve the equation using basic algebra.  It is straightforward, but tedious, because the numbers are not "nice".<br>
I leave it to you to finish the solution by that method; it's good practice in basic algebra for you.<br>
(2) A quick and easy informal way to solve mixture problems like this....<br>
The ratio in which the two ingredients have to be mixed is exactly determined by where the 75% of the mixture lies between the 70% and 95% of the two ingredients.<br>
(a) 75% is 1/5 of the way from 70% to 95%.  (70 to 95 is a difference of 25; 70 to 75 is a difference of 5; 5/25 = 1/5.)
(b) That means 1/5 of the mixture has to be the higher percentage ingredient.<br>
ANSWER: 1/5 of 130 ounces, or 26 ounces, of 95% juice; the other 104 ounces of 70% juice.<br>
CHECK:
.95(26)+.70(104) = 24.7+72.8 = 97.5
.75(130) = 97.5<br>