SOLUTION: If 4 liters of a 15% vinegar solution is mixed with x liters of a 30% vinegar solution, the result is a 20% vinegar solution. How many liters of the 30% vinegar solution were mixed

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Question 1196283: If 4 liters of a 15% vinegar solution is mixed with x liters of a 30% vinegar solution, the result is a 20% vinegar solution. How many liters of the 30% vinegar solution were mixed?
The mixture required _ liter(s) of the 30% solution
Found 2 solutions by amoresroy, math_tutor2020:
Answer by amoresroy(361) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of liters of 30% vinegar as solution
Expressing the problem into equation:
0.15(4) + 0.3x = 0.2(4 + x)
0.6 + 0.3x = .8 + .2x
Combine like terms:
0.3x - 0.2x = 0.8 - 0.6
0.1x = 0.2
x = 0.22/0.1
x = 2
Answer:
The mixture required 2 liters of the 30% solution.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Algebraic approach:

x = number of liters of the 30% vinegar solution

0.30x = amount of pure vinegar from that 30% solution

We have 4 liters of a 15% solution, so we add on 4*0.15 = 0.60 more liters of pure vinegar.

In total we have 0.30x+0.60 liters of pure vinegar.

There are x liters of the 30% solution and 4 liters of the 15% solution. That gives x+4 total liters of solution (pure vinegar + other stuff)
We want this total to have a 20% vinegar solution, so we want 0.20(x+4) liters of pure vinegar.

We have these two expressions
0.30x+0.60
0.20(x+4)
which represent the total amount of pure vinegar we're after

Set them equal to each other and solve for x.
0.30x+0.60 = 0.20(x+4)
0.30x+0.60 = 0.20x+0.20*4
0.30x+0.60 = 0.20x+0.80
0.30x-0.20x = 0.80-0.60
0.10x = 0.20
x = (0.20)/(0.10)
x = 2

We require 2 liters of the 30% solution

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A different approach:

The target is 20% solution

The gap from 15% to 20% is 5
The gap from 30% to 20% is 10

Then form a ratio by listing the results in reverse order
We get the ratio 10:5 which simplifies to 2:1

This means that we need twice as much of the 15% solution compared to the 30% solution
Flipped around: we'll need half as much of the 30% solution compared to the 15% solution.

We have 4 liters of the 15% solution
So we need (1/2)*4 = 2 liters of the 30% solution

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Answer: 2 liters of the 30% solution