Write a linear system.

Question

I need homework help fast.The manager of a fish store has water that is 15% salt and water that is 30% salt. He needs to fill an aquarium with 6 gallons of water that is 25% salt.
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.
 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 = the number of gallons of 15% (0.15) salt water and y = the number of gallons of 30% (0.30) salt water.

 

x + y = 6 gallons  (hence x = 6-y)

(0.15)x + (0.30)y = (0.25)*(6 gallons)

 

To solve, substitute 6-y in place of x:

 

(0.15)(6-y) + 0.3y = 1.5

0.9 - 0.15y + 0.3y = 1.5

0.15y = 0.6

y = 4 gallons

 

x = 6-4 = 2 gallons