2. 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.
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.
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umm ok wow, hold on i'll try and solve it
10 percent 5/3 gallons
25 percent 10/3 gallons
Do you understand it now?
Let x = amount of 10% salt and y = amount of 25% salt
x + y = 5
Two ways (which are quite equivalent):
#1: Find ratio of x to y, independent of the actual volume:
x / 10 + y / 4 = (x + y) / 5
4x + 10y = 8x + 8y
4x = 2y
y = 2x
Then bring in the total volume: x + y = 5
x + 2x = 5
3x = 5, x = 5/3, y = 2x = 10/3
#2 More traditional method
y = 5 - x
(Salt from x) + (salt from y) = (total salt in the mix)
.10 x + .25 (5 - x) = .2 * 5 = 1
10x + 125 - 25x = 100
-15x = -25
x = 5/3
y = 5 - 5/3 = 10/3
that might help