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Question

A scientist needs 480 liters of a 30% alcohol solution. She has available a 65% and a 25% solution. How many liters of the 65% and how many liters of the 25% solutions should she mix to make the 30% solution? Write an equation for the total amount of the solution liters and another equation for the amount of alcohol, and then solve the system to determine how many liters of each alcohol solution was used.

let x represent the number of liters for 65% alcohol solution and Y represent the number of liters for 25% alcohol solution.



The equation that describes the total amount of liters is__________________

The equation that describes the amount of alcohol is___________________

The scientist needs ____________liters of 65% alcohol solution and________liters of 25%alcohol solution

Answer 1

.65x + .25(480-x) = .30(480) is an equation describing the amount of alcohol

.65x -.25x = .30(480) -.25(480)

.4x = .05(480)

x = .05(480)/.4 = .05(120)/.1 = .5(120)

= 60 Liters of 65%

mixed with 420 Liters of 25%

gives 480 Liters of 30%

.65(60) +.25(420 = .30(480) is an equation describing the amount of alcohol

39 + 105 = 144 = 3(48) = 144 Liters of alcohol

30 is within 5 of 25

65 is within 35 of 30

35/5 =7

you need 7 times as much of 35% as of 65

420 = 7(60)

60L of 65%+ 420L of 25% = 480L of 30%

60L + 420L = 480L is an equation describing the amount of Liters