Question 1142434: You need to prepare a 30 mL solution of a 1:6 syrup solution. You have on hand a 50% syrup solution, and a 1:200 soda solution. How many mL of each solution do you need to create this final solution?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'll take a stab at this even though i'm not totally sure it will be correct.
as i understand the problem:
you want your final solution to have a ratio of 1 part syrup to 6 parts soda.
you have two solutions on hand.
one of them is 50% syrup which presumably means it has 1 part syrup to 1 part soda.
the other has 1 part syrup to 200 parts soda.
your final solution has to be 30 milliliters total.
if your final solution is 30 milliliter total, and it has to be 1 part syrup and 6 parts soda, then 1/7 of the final solution must be syrup and 6/7 of the final solution should be soda.
1/7 * 30 = 4.285714286 milliliters of pure syrup.
let x = the number of liters of the 50% syrup solution.
let y = the number of liters of the 1 part syrup to 200 parts soda solution.
the ratio of syrup to total solution of the 50% solution is 1/2.
the ratio of syrup to total solution of the 1 part syrup to 200 parts soda solution is 1/201.
your equation becomes 1/2 * x + 1/201 * y = 1/7 * 30
you also have x + y = 30 because the total number milliliters of both needs to be 30.
these 2 equations need to be solved simultaneously.
they are:
1/2 * x + 1/201 * y = 1/7 * 30
x + y = 30
solve for y in the second equation to get y = 30 - x
replace y with 30 - x in the first equation to get:
1/2 * x + 1/201 * (30 - x) = 1/7 * 30
multiply both sides of this equation by 2814 to get:
1/2 * 2814 * x + 1/201 * 2814 * (30 - x) = 1/7 * 2814 * 30
simplify to get:
1407 * x + 14 * (30 - x) = 12060
simplify further to get:
1407 * x + 420 - 14 * x = 12060
combine like terms to get:
1393 * x + 420 = 12060
subtract 420 from both sides of this equation to get:
1393 * x = 11640
solve for x to get:
x = 11640 / 1393 = 8.356066045.
y = 30 - x, therefore y must be equal to 21.64393396.
your final solution will be 30 milliliters total.
it will contain 8.35606045 milliliters of the 50% syrup solution.
it will contain 21.64393396 milliliters of the 1 part syrup to 200 parts soda solution.
your total amount of syrup in the final solution will therefore be:
.5 * 8.35606045 + 1/201 * 21.64393396 = 4.285714286 milliliters of pure syrup.
4.285714286 / 30 = .1428571429
that's the ratio of pure syrup to total solution in your final solution.
multiply that by 7/7 and you get 1/7, which is the desired ratio of pure syrup to total solution in the final solution.
if 1/7 of the total is purse syrup, then 6/7 of the total is purse soda.
the ratio of syrup to soda is (1/7) / (6/7) = (1/7) * (7/6) = 1/6 which means 1 part syrup to 6 parts soda which is what you want.
this is what i think your answers should be.
the concept is sound if my understanding of the problem is correct.
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