3. The manager of a fish store has water that is 10% salt and water that is 25% salt. He needs to fill an aquarium with 5 gallons of water that is 20% salt.

Question

a.     Write a system of linear equations that you can use to determine how many gallons of each type of salt water the manager should combine. Be sure to define your variables.

b.    Solve the system and determine how many gallons of each type of salt water the manager should combine. Show all your work.

Answer 1

Let x = number of gallons of water that is 10% salt

Let y - number of gallons of water that is 25% salt

 x + y = 5    Solve for x          x = 5 - y

.10x + .25y = .20(5)   Multiply both sides by 100 to remove the decimal points

10x + 25y = 20(5) = 100     Divide both sides by 5

2x + 5y = 20      Replace x with 5 - y

2(5 - y) + 5y = 20

10 - 2y + 5y = 20

3y = 10

y = 3 1/3 gallons

 

x = 5 - 3 1/3

x = 1 2/3 gallons