write a system of linear equations

Question

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. Write a system of linear equations, solve the system and determine how many gallons of each type of salt water the manager should combine.

Answer 1

X=number of gallons of 10%, Y = number of gallons of 25%.  Since total number of gallons = 5, then
X+Y = 5 (EQ1)   The salt content of the final mixture is 5 times 0.20 = 1.
So  0.10X + 0.25Y = 1 (EQ2) and these (EQ1 & EQ2) are your system of equations.
Solve by Substitution.  From EQ1, X = 5-Y, is substituted in EQ2:
0.10 (5-Y) + 0.25Y = 1  and 0.5-0.10Y+0.25Y=1  and 0.15Y = 0.5; Y = 10/3 gallons; X = 5-(10/3)= 5/3 gallons.  Answer 5/3 gallons of 10%, 10/3 gallons of 25%