SOLUTION: A chef needs 6 L of a solution that is 70% sugar. He has a 30% sugar mixture and an 80% sugar mixture that he can combine to make the 70% mixture. Let x represent the number of

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Question 1133340: A chef needs 6 L of a solution that is 70% sugar. He has a 30% sugar mixture and an 80% sugar mixture that he can combine to make the 70% mixture.
Let x represent the number of liters of the 30% sugar mixture and let y represent the number of liters of the 80% sugar mixture.
How many liters of each solution will he use?
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=0.30 mixture y=0.80 mixture
x+y=6
y=(6-x)
.30x+.80(6-x)=6(.70), pure sugar equation
.30x+4.8-0.80x=4.20
-.50x=-.60
x=1.2 liters of 30% and 6-x or y=4.8 liters of 80%.
check 70% is 4/5 of the way between 30% and 80%
want 4/5 of the 80% and 1/5 of the 30%

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = 30% solution
y = 80% solution.

you want 6 liters of a 70% solution.

first equation is x + y = 6

second equation is .3 * x + .8 * y = .7 * (x + y)

in the first equation solve for y to get y = 6 - x

in the second equation replace y with 6 - x to get:

.3 * x + .8 * y = .7 * (x + y) becomes .3 * x + .8 * (6 - x) = .7 * (x + 6 - x)

simplify to get .3 * x + 4.8 - .8 * x = 4.2

combine like terms to get: -.5 * x + 4.8 = 4.2

subtract 4.8 from both sides of this equation to get -.5 * x = -.6

divide both sides of this equation by -.5 to get:

x = -.6/-.5 = 1.2

in the equation of x + y = 6, replace x with 1.2 and solve for y to get:

y = 6 - 1.2 = 4.8

x + y = 6 becomes 1.2 + 4.8 = 6 which becomes 6 = 6 which is true.

.3 * x + .8 * y = .7 * (x + y) becomes .3 * 1.2 + .8 * 4.8 = .7 * (1.2 + 4.8) which becomes .36 + 3.84 = .7 * 6 which becomes 4.2 = 4.2 which is true.

the solution looks good.

x = 1.2 and y = 4.8

x + y = 6 becomes 1.2 + 4.8 = 6 which is true.

.3 * x + .8 * y becomes .3 * 1.2 + .8 * 4.8 which becomes .36 + 3.84 which becomes 4.2

4.2 / 6 = .7 = 70% which satisfies the requirements of the problem.

1.2 liters of a 30% mixture added to 4.8 liters of an 80% mixture results in 6 liters of a 70% solution.