SOLUTION: A 15% lemon solution is added to a 5% lemon solution with the same amount in order to achieve a 10 liter of lemon solution with 10% concentration. How much 15% lemon solution w

Question 1173603: A 15% lemon solution is added to a 5% lemon solution with the same amount in order to
achieve a 10 liter of lemon solution with 10% concentration. How much 15% lemon
solution was initially present?
Found 4 solutions by Theo, MathTherapy, ikleyn, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = number of liters of 15% lemon solution mixture.
y = number of liters of 5% lemon solution mixture.

your equations are:
x + y = 10
.15x + .05y = .10 * (x + y) = .10 * 10 = 1

the first equation tells you the total number of liters in the mixture.
the second equation tells you the amount of lemon solution in the mixture.

the equations become:
x + y = 10
.15x + .05y = 1

multiply both sides of the first equation by .15 and leave the second equation as is to get:

.15x + .15y = 1.5
.15x + .05y = 1

subtract the second equation from the first to get:

.10y = .5
solve for y to get:
y = 5

since x + y = 10, then x must also be equal to 5.

your answer is that 5 liters of the 15% solution must have been there initially.
you then added the same amount of liters of the 5% solution to get a total number of liters equal to 10 that is 10% solution.

x + y becomes 5 + 5 = 10
.15 * x + .05 * y becomes .15 * 5 + .05 * 5 which becomes .75 + .25 = 1

you have 1 liter of lemon solution in 10 liters of mixture = 10% lemon solution.

since the problem stated that you were adding the same amount of the 5% solution to the 15% solution, and the total number of liters of the mixture needs to be 10, then you could have come up with your answer as follows.

let x = the number of liters of the 15% solution.
let x also = the number of liters of the 5% solution.

your equation becomes:

2x = 10
solve for x to get 5.

your answer would be 5 liters of 15% plus 5 liters of 5% solution.

you would then confirm by taking .15 * 5 and adding .05 * 5 to get .75 + .25 = 1 liter of lemon solution.
1 / 10 = .10 = 10% lemon solution.

it's more direct, assuming you understood the problem statement correctly.

if not, the general solution (using x and y) would get you the same answer, as i showed above.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A 15% lemon solution is added to a 5% lemon solution with the same amount in order to
achieve a 10 liter of lemon solution with 10% concentration. How much 15% lemon
solution was initially present?

You DON'T need to write a NOVEL, and go through complex calculations as the other person did. Unless of course,
you're asked to form equations and solve for the initial amount of 15% solution.
Having said that, 15% down to 10% results in a 5% reduction, and 5% up to 10% results in a 5% increase.
Since the reduction and increase in percentages are the same, then EQUAL amounts were INITIALLY mixed, so .
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.

Actually, it is A JOKE PROBLEM,

because the answer is known to every housewife, based on her common sense,
as I once noticed before, answering this question couple of days ago (I am lazy to search for this link . . . ).

There is no need to solve equation/equations in this case - the answer should be OBVIOUS based on common sense.

But some people do not distinct a joke from a real problem . . .

The intention of this problem is simply to check if a recipient has enough common sense to answer momentarily . . .

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
The 10% wanted is exactly between the available 15% and the 5%.
Ten liters is wanted.

"Same amount" of each of the starting lemon solutions, so 5 liters of 15% and 5 liters of 5%.
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