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 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

@TheSmartOne

Answer 2

@mathstudent55 @phi @zepdrix

Answer 3

@BGrg007

Answer 4

There is a pattern for this type of problem
the first thing is to define two variables for the amount of each type. For example,
x = # of gallons of 10% salt water
y = # of gallons of 25% salt water

Answer 5

Yes that is what I first thought but I didn't know how to setup the equation

Answer 6

if you use x gallons of the one type and y gallons of the other type
how many gallons total are you using ? any idea ?

Answer 7

x + y ?

Answer 8

yes
now notice this
He needs to fill an aquarium with 5 gallons of water

how much do you want x+y to equal ?

Answer 9

5

Answer 10

yes. can you write an equation showing that ?

Answer 11

so x + y = 5

Answer 12

yes. now we need one more equation. we do that by figuring how much salt we have

look at
5 gallons of water that is 20% salt.
any idea how much salt that is ?

Answer 13

1 gallon

Answer 14

yes, or 5 gallons * 0.20
(we need to know that "formula" to write how much salt is in the x gallons of 10% salt)
any idea ?

Answer 15

5 times 0.10?

Answer 16

oh

Answer 17

almost, but x is not 5 gallons. x is some # of gallons (which we don't know)

Answer 18

x times 0.10

Answer 19

yes
and use the same idea for how much salt is in the y gallons (of 25% salt)

Answer 20

so

\[x \times 0.10\]

and

\[y \times 0.25\]

Answer 21

and the sum of that salt must equal 5*0.2 = 1

Answer 22

ohhhhhh

Answer 23

\[0.10x + 0.25y = 1 \]

Answer 24

yes, now you have two equations and two unknowns.

Answer 25

\[x + y = 5\]

Answer 26

Ok, now I have to solve

Answer 27

if you mulitply the 0.1x+0.25y= 1
by 100 (on both sides, and all terms)
we get
10x+25y= 100
which gets rid of the decimals
now you have
10x+25y= 100
x+ y= 5
if you multiply the bottom equation by -10 (on both sides, all terms)
what do you get ?

Answer 28

-10x -10y = -50

Answer 29

So eliminate?

Answer 30

yes, now add the two equations
the 10x -10x will cancel

Answer 31

15y = 50

Answer 32

yes, now divide both sides by 15
on the left 15/15 is 1

Answer 33

y = 3.3?

Answer 34

wait

Answer 35

yeah y = 3.3

Answer 36

x + 3.3 = 5

x = 1.7

Answer 37

I would use 10/3 or 3 and 1/3
rather than a decimal

Answer 38

Because of the perpetual 3?

Answer 39

yes

Answer 40

y = 3 and 1/3

x = 1 and 2/3

Answer 41

yes, that is the answer

Answer 42

Thank you @phi I really appreciate your help, I couldn't get my head around this one

Answer 43

yw

Answer 44

Will you be on more today?

Answer 45

I have to brb for 5min but I might need more help as I'm going through these hard lessons

Answer 46

ok