Question

Can anyone help me on a linear equation problem....I'll post the question

Answer 1

Did you define your variables?

Answer 2

you mean like x and y?

Answer 3

x and y don't mean anything until you say what they stand for.

Answer 4

.10x + .25y = ? that's what I got so far

Answer 5

what does x stand for ?

Answer 6

10% salt

Answer 7

?

Answer 8

the question is
how many gallons of each type (of salt water) should be combined

How about x is the number of gallons of 10% saltwater
and y is the number of gallons of 20% saltwater.

any idea what you want x and y to combine to ?

Answer 9

you are going to pour x gallons into the tank and then another y gallons (you don't know how much x and y are) but what do they add up to ?

Answer 10

you would want them add up to 5 gallons of water?

Answer 11

yes,
Can you write that as an equation ?

Answer 12

as the linear equation?

Answer 13

yes.

Answer 14

If you had numbers like 1 and 4 you could write it as 1+4=5
but you don't have numbers, you have letters. But it is the same idea

Answer 15

okay I got that part
now I have to solve the equation

Answer 16

what do you have ?

Answer 17

I have .10x + .20y = 5

Answer 18

that is not quite right. You will have an equation (sort of) like that.
But first, work on this one:

you have x gallons of saltwater (10% strength) and y gallons of saltwater
you add them together to get 5 gallons of saltwater
can you say that same idea as an equation ?

Answer 19

so x = 10% saltwater
y = 25% saltwater...?

sorry haven't done these problems in awhile

Answer 20

almost. x is the number of gallons (of 10% saltwater)
y is gallons (of 25% saltwater)

If you had to drink x gallons and then later drank y gallons how many gallons did you drink ?

Answer 21

x +y = 5 gallons?

Answer 22

yes, that is the way to write it
(the only way we know x+y is 5 is because we know it fills the fish tank which is 5 gallons)

Answer 23

we have two unknowns: x and y
that means (it always means) you need to equations

we have one equation x+y=5

now we need another equation

Answer 24

*two equations

the other equation is going to be using the idea that we can add up the *salt*

how much of the water in the fish tank is going to be salt ?

Answer 25

so equation 1 is x + y = 5
2. .10x + .25y = .20?

Answer 26

2nd equation*

Answer 27

closing in on it.

But it helps to have the *big idea*.

They tell you they want 5 gallons that is 20% salt
that means 20% of the 5 gallons is salt
how much salt is that ?

Answer 28

20% of the 5 gallons

this is arithmetic, you get a number

Answer 29

A x = 10% saltwater
Y = 25% saltwater
x + y = 5 gallons
.10x (saltwater) + .25y ( saltwater) = 5 gallons

Answer 30

that's what I got for the first part of the problem

Answer 31

yes, and that is close.
But you should think about this question:
20% of the 5 gallons is salt
how much salt is that ?

Answer 32

wouldn't it be .20?

Answer 33

let me ask it this way
(we know 20% is 0.20 or 20/100 or 1/5)
1/5 of the 5 gallons is salt
how many "gallons" of salt do we have ?

Answer 34

1 gallon?

Answer 35

yes. 1 gallon. you could write
20% of 5 is 0.20*5 = 1 gallon

how much salt is 10% of x gallons ?
we can't get a number but it is the same idea 0.10x
is the amount of salt in the 10% saltwater

0.25y is the amount of salt in the 25% saltwater

and common sense tells you the amount of salt in the x gallons plus the amount of salt in the y gallons must add up to the amount of salt in the 5 gallons

Answer 36

can you write your 2 equations ?

Answer 37

okay
.20 X 5 = 1 gallon
.10x + .25y = 5 gallons

Answer 38

I guess you are not seeing that the second equation
is adding up the salt in both concentrations. the right hand side of
.10x + .25y = ??
is not 5 gallons (of saltwater)
it is the number of "gallons" of salt in the 5 gallons of saltwater

Answer 39

OHHHH okay I didn't get that part

Answer 40

and this for part b ?

Answer 41

this is (a)

the two equations are
x+y= 5
0.1x + 0.25y= 1 <-- notice 1 because this is 0.20*5

Answer 42

for (b), you "solve" these equations.

Answer 43

Okay I get that

Answer 44

x=1.6667
y=3.3333 ....?

Answer 45

I don't like decimals, so if we multiply the 2nd equation by 10
(that means both sides, all terms we get)
x + 2.5y= 10


we now have
x + 2.5y= 10
x+ y= 5

if we subtract the bottom equation from the top we get
1.5 y = 5
y= 5/1.5= 3 1/3 or 10/3

x= 5- 3 1/3= 1 2/3 or 5/3

Answer 46

yes, you got the correct answer.

All these "mixture" problems use the same idea, so if you review how you did this one, you should be able to figure out the next one you tackle.

Answer 47

Okay thank you so much....sorry for taking up so much of your time

Answer 48

yw

Answer 49

ok

Answer 50

yeah. 1 gallon. you could write 20% of 5 is 0.20*5 = 1 gallon how much salt is 10% of x gallons ? we can't get a number but it is the same idea 0.10x is the amount of salt in the 10% saltwater 0.25y is the amount of salt in the 25% saltwater and common sense tells you the amount of salt in the x gallons plus the amount of salt in the y gallons must add up to the amount of salt in the 5 gallons