Question

For his chemistry experiment, Martin needs 3 liters of a 40% alcohol solution. The lab has two containers, one with 20% alcohol solution and the other with 50% alcohol solution.

a.) Write a system of linear equations that you can use to determine how many liters of each type of alcohol solution Martin should combine to get 3 liters of a 40% alcohol solution. Be sure to define your variables.
b.) Solve the system and determine how many liters of each type of alcohol solution Martin should combine. Show all your work.

Answer 1

let the amount of the 20% be x and the amoount of 50% by y and

needs 3 liters
x+y=3

also
and the amount is 0.40*3lliters

find
x and y
such that
x+y=3 and
0.4*3=0.2y+0.5x
1.2=0.2y+0.5x
firs tmulitply second equaoitn by 10
12=2y+5x
5x+2y=12
so

x+y=3

multiply this equaoitn by -2 and add to other equaiton

-2x-2y=-6
5x+2y=12 +
3x+0y=6

3x=6
divide both sides by 3
x=2

sub back
x+y=3
2+y=3
minus 2 both sides
y=1


2 liters of 40%
1 liter of 20%


a.
x+y=3
0.5x+0.2y=0.4*3

b. 2 liters of 40%, 1 liter of 20%

x=3

sub back

x+y=3

Answer 2

Let the amount of 40% solution be a and 80% solution b.

so, 0.4a + 0.8b = 0.5(a + b)

Now, a + b = 2

=> 0.4a + 0.8(2 - a) = 0.5(2)

i.e. 1.6 - 0.4a = 1

so, 0.4a = 0.6

=> a = 1.5 and b = 0.5

Hence, 1.5 litres of 40% solution needs mixing with 0.5 litres of 80% solution to give a 2-litre, 50% solution