SOLUTION: To create a breakfast beverage, kiwi juice in two concentrations, 14% and 40%, must be combined into a solution that will be mixed with another type of juice to produce the beverag
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Question 837699: To create a breakfast beverage, kiwi juice in two concentrations, 14% and 40%, must be combined into a solution that will be mixed with another type of juice to produce the beverage. If 60 gallons of 14% juice is used, how many gallons of the 40% juice must be used to obtain a 30% kiwi juice solution?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = number of gallons of 40% kiwi juice mixture.
you have 60 gallons of 14% kiwi juice mixture.
you have x gallons of 40% kiwi juice mixture.
you want to have (x + 60) gallons of 30% kiwi juice mixture.
your total mixture will contain x + 60 gallons.
30% of that should be kiwi juice.
this means that the amount of kiwi juice in the total mixture must be equal to .3 * (x + 60) which is equal to .3x + .3*60 which is equal to .3x + 18 gallons of kiwi juice.
60 gallons of 14% kiwi juice will be mixed with x gallons of 40% kiwi juice to make a mixture that has 30% kiwi juice.
since 30% kiwi juice has been calculated to be equal to .3x + 18, your formula will be.
.14 * 60 + .4x = .3 * (x + 60) which becomes:
.14 * 60 + .4x = .3x + 18
you need to simplify and solve for x.
you will get the following:
start with:
.14 * 60 + .4x = .3x + 18
simplify to get:
8.4 + .4x = .3x + 18
subtract .3x from both sides of this equation and subtract 8.4 from both sides of this equation to get:
.4x - .3x = 18 - 8.4
simplify to get:
.1x = 9.6
divide both sides of this equation by .1 to get:
x = 9.6 /.1
this makes x equal to 96 gallons of of 40% mixture.
you will be mixing 60 gallons of 14% mixture with 96 gallons of 40% mixture to get a combined total of 156 gallons of 30% mixture.
to confirm, replace all variables with their known values and solve.
formula is:
.14 * 60 + .4 * 96 = .3 * 156
simplify to get:
8.4 + 38.4 = 46.8
combine like terms to get:
46.8 = 46.8
the solution of 96 gallons of 40% mixture has been confirmed to be good.
the answer to the question is:
you will need 96 gallons of 40% juice to obtain a 30% kiwi juice solution.
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