SOLUTION: One drink contains 5% fruit juice and another contains 50% fruit juice. How many gallons of each type should be combined to make 5 gallons of a drink that contains 40% fruit juice?
Question 1129795: One drink contains 5% fruit juice and another contains 50% fruit juice. How many gallons of each type should be combined to make 5 gallons of a drink that contains 40% fruit juice? (Please solve this using substitution method.) Answer by ikleyn(52782) (Show Source):
Let x be the amount (= the volume) of the 5% fruit juice (in gallons), and
let y be the amount (= the volume) of the 50% fruit juice.
Then you have two equations
x + y = 5 gallons (1) (the total volume)
0.05*x + 0.50*y = 0.4*5 gallons (2) (the volume of the pure juice).
The setup is completed.
To solve the system, I will apply the Substitution method.
For it, express x = 5-y from the first equation and substitute it into the second equation, replacing x. You will get
0.05*(5-y) + 0.5*y = 0.4*5
0.25 - 0.05y + 0.5y = 2,
0.45y = 2 - 0.25
0.45y = 1.75 ====> y = = = = = = = .
Answer. of the 50% fruit juice and the rest - = gallons of the 5% fruit juice.
Check. Equation (1): + = 5. ! Correct !
Equation (2): Left side of the eq. (2) is + = = = 2 gallons of the pure juice.
Right side of the eq(2) is 0.4*5 = 2 gallons of the pure juice.
Both sides are equal <--------> the solution (the answer) is correct !
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