Math Genuises!!! PLEASE help me!!!!?

Question

A juice drink manufacturer has found mixing kiwi juice concentrate and fresh squeezed orange juice is the most cost effective way to produce its breakfast beverage. the kiwi juice comes in two concentrated foms, 17% and 30% kiwi juice, whice must be combined into a solution that can be mixed with the orang juice. if 50 gallons of 17% juice is used, how many gallons of the 30% juice must be used to obtain a 20% kiwi juice solution?

i dont get this at all!!! so much words are used in this and it is very confusing for me!!! T-T . please explain step by step for me to get it!! thanks!!!

Answer 1

You can work it as an algebra problem, but it helps if you understand what is going on. If you start with 50 gallons of 17% concentrate and start adding 30% a gallon at a time and some how measure the concentration (after stirring well) it should be clear that the concentration as well as the total amount of concentrate is going to get higher. After you have added 1 gallon of 30% you will have 51 gallons of something like 17.255% concentration (see below). If you keep on going, eventually you will get to 20% concentration.
50*0.17 + x*0.30 = (50+x)*.20
solve for x

Below: there are 8.5 gallons of kiwi juice in the 50 gallons of 17% concentrate (just multiply). In one gallon of 30% concentrate, there are 0.3 gallons. Add the two together and divide by 51 gallons total to get the concentration.

Answer 2

Let x = the number of gallons of 30% to be added
50 gallons * 17% + x *30% = (50+x)*20%
So change % to decimals getting:
50*.17 + .3x = .2*50 +.2 x
8.5 +.3x = 10 +.2x
.3x - .2x = 10 - 8.5
.1x = 1.5
x = 15 gallons of 30% kiwi juice must be added

Answer 3

The 50 gallons of 17% juice contain 0.17*50 = 6.5 gallons of pure juice. Suppose you add X gallons of 30% juice. That would be another 0.3X gallons of pure juice. So the total number of gallons of pure juice you'd have would be 6.5 + 0.3X. The total number of gallons of diluted juice you'd have would be 50+X. You want a 20% solution, so you'd want 0.2(50+X) = 6.5 + 0.3X ==> 10 + 0.2X = 6.5 + 0.3X ==> 0.1X = 3.5 ==> X = 35 ==> add 35 gallons of 30% juice.