A scientist needs 400 liters of a 55% alcohol solution. She has available a 75% and a 25% solution.

Question

A scientist needs 400 liters of a 55% alcohol solution. She has available a 75% and a 25% solution. How many liters of the 75% and how many liters of the 25% solutions should she mix to make the 55% 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 75%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 75% alcohol solution and________ liters of 25% alcohol solution.



please answer the blanks and also explain to me in detail please thank you

Answer 1

,75x + .25(400-x) = .55(400)

.75x - .25x = .55(400) -.25(400

.5x = .3(400) = 120

x = 240 liters of 75%

mixed with

160 liters of 25%

.75(240) + .25(160) = 180+ 40 = .55(400) = 220

equation for total amount of liters is

240 + 160 = 400 liters of 55%

75 is within 20 of 55

25 is within 30 of 55

20/30 = 2/3 = 160L/240L