t 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. Show all your work.

Okay for part a, I got:

x+y=5

.10x+.25y=20

Question

t 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. Show all your work.


Okay for part a, I got:

x+y=5

.10x+.25y=20

inexilewetrust · Answer

@icecreamman

elonasushchik · Answer

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

anonymous · Answer

ok are you like for sure that your part a is right?

inexilewetrust · Answer

Yeah, my teacher confirmed it.

inexilewetrust · Answer

But she didn't go to part B.

anonymous · Answer

nice copying and pasting @ElonaSushchik lol

anonymous · Answer

ok lemme think

anonymous · Answer

so at the end of the second equation that you got, are you sure its not 0.10x + 0.25y = (0.2)(x + y)

inexilewetrust · Answer

No, the teacher said it was the equation I mentioned.

inexilewetrust · Answer

But it can be solved different ways.

inexilewetrust · Answer

I think it might be that. I am not sure. All I  know is the answer the other person posted is correct but I need to explain the steps as to how I got my answer.

inexilewetrust · Answer

Just realized the question didn't come out as one.

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.

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.