Mathematics, 24.11.2019 06:31, ptrlvn01

a chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 80% pure antifreeze. the company wants to obtain 240 gallons of a mixture that contains 35% pure antifreeze. how many gallons of water and how many gallons of the premium antifreeze solution must be mixed?

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Company will need 105 gallons of premium antifreeze solution. And 135 gallons of water to be mixed to get a solution which contains 84 gallons of pure antifreeze in 240 gallon mixture that 240 gallons of a mixture that contains 35% pure antifreeze.

Solution:

Given that chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture.

The premium antifreeze solution contains 80% pure antifreeze.

The company wants to obtain 240 gallons of a mixture that contains 35% pure antifreeze.

Need to calculate gallons of water and gallons of the premium antifreeze solution must be mixed to get 240 gallons of 35% pure antifreeze.

Lets first calculate quantity of pure antifreeze required for 240 gallons having 35% of pure antifreeze.

35% of 240 gallons = 0.35 x 240 = 84 gallons of pure antifreeze.

Now need to determine quantity of premium antifreeze solution which will containing 84 gallons of pure antifreeze.

As premium antifreeze solution contains 80% pure antifreeze

=> 1 gallon of premium antifreeze solution contains 80% of 1 gallon of pure antifreeze

=> 1 gallon of premium antifreeze solution contains 0.8 gallons of pure antifreeze

=> number of gallons of premium antifreeze solution which contains 0.8 gallons of pure antifreeze = 1

So number of gallons of premium antifreeze solution which contains 1 gallons of pure antifreeze $=\frac{1}{0.8}=\frac{10}{8}=1.25 \text { gallons }$

=> Number of gallons of premium antifreeze solution which contains 84 gallons of pure antifreeze

= 84 x number of gallons of premium antifreeze solution which contains 1 gallons of pure antifreeze

= 84 x 1.25 = 105 gallons of premium antifreeze solution.

So company will need 105 gallons of premium antifreeze solution.

And (240 – 105 ) = 135 gallons of water to be mixed to get a solution which contains 84 gallons of pure antifreeze in 240 gallon mixture that 240 gallons of a mixture that contains 35% pure antifreeze.

answered: Guest

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.