Question 1024640: How many ounces of a 45% alcohol solution must be mixed with 18 ounces of a 50% alcohol solution to make a 46% alcohol solution?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of ounces of the 45% solution.
let y = the number of ounces of the 46% solution.
your formula is:
.45 * x + .50 * 18 = .46 * y
you have another formula.
that formula is:
x + 18 = y
the first formula is telling you the amount of alcohol.
the second formula is telling you the amount of solution.
these equations need to be solved simultaneously.
this means the same solution applies to both.
the equations are:
.45 * x + .50 * 18 = .46 * y
x + 18 = y
the first equation can be simplified to get:
.45 * x + 9 = .46 * y
x + 18 = y
you can replace y in the first equation with the equivalent value of y from the second equation to get:
.45 * x + 9 = .46 * (x + 18).
simplify this equation to get:
.45 * x + 9 = .46 * x + .46 * 18.
simplify further to get:
.45 * x + 9 = .46 * x + 8.28.
subtract .45 * x from both sides of the equation and subtract 8.28 from both sides of the equation to get:
9 - 8.28 = .46 * x - .45 * x.
simplify to get:
.72 = .01 * x
divide both sides of this equation by .01 to get:
.72 / .01 = x
solve for x to get:
x = 72.
go back to your original equations and replace x with 72.
your original equations are, after they have been simplified:
.45 * x + 9 = .46 * y
x + 18 = y
replace x with 72 and you get:
.45 * 72 + 9 = .46 * y
72 + 18 = y
in the second equation, you get y = 90.
solve for y in the first equation to get:
y = (.45 * 72 + 9) / .46 = 90.
you have:
x = 72
y = 90
let x = the number of ounces of the 45% solution = 72.
let y = the number of ounces of the 46% solution = 90.
you were asked for how many ounces of the 45% solution were required.
the answer is 72.
|
|
|
