Question

Hey guys I have a question on Application of linear equations?

Answer 1

Here is the problem

Answer 2

were you able to get anywhere with this?

Answer 3

Well I got that x + y would have to equal $345

Answer 4

x is the amount you invest at 8%
y is the amount you invest at 3%

agreed so far?

Answer 5

yes

Answer 6

so x+y is the total amount you invested

Answer 7

8000 is the total amount of money you have to invest

Answer 8

so the two must be the same, so

x+y = 8000

Answer 9

make sense?

Answer 10

Yes so far

Answer 11

ok great

Answer 12

if x is the amount you invest at 8%, then you earn 0.08x dollars in interest just from that account

Answer 13

if y is the amount you invest at 3%, then you earn 0.03y dollars in interest just from that account

Answer 14

in total, you earn 0.08x + 0.03y dollars in interest from both accounts

Answer 15

it's given that you earn $345 in interest, so

0.08x+0.03y = 345

Answer 16

Ohhh so the x and y values are interest?

Answer 17

no those are the amounts invested

Answer 18

Oh okay

Answer 19

if the total was 8,000 how did she only get 345?

Answer 20

well that's how investments work

you'll never get a 100% return all the time (unless you get really lucky)

Answer 21

so you have to wait to earn all your money back (and then some)

Answer 22

Ohhh okay makes sense I don't know anything about investments

what equation do I use to solve this?

Answer 23

you would solve the system of equations for x and y

x+y = 8000
0.08x+0.03y = 345

Answer 24

the answer for y will be the answer they want

Answer 25

when I solve the equation I would make the percentages into fractions or?

Answer 26

you could, or you could leave the decimals as they are

Answer 27

okay let me try that

Answer 28

alright

Answer 29

I got x = 2,100 and for y = 5,900

Answer 30

ok let me check

Answer 31

kk

Answer 32

very good, so the answer they want is just 5900

Answer 33

since that's the amount you invest at 3%

Answer 34

I still don't get investments lol but glad I got the problem right

Answer 35

well you're on your way to understanding them better

Answer 36

Thanks I was wondering if you could help me on one more problem?

Answer 37

sure

Answer 38

Thanks

Answer 39

let

x = amount of solution that's 5% salt
y = amount of solution that's 25% salt

both amounts are in liters


you need 10 liters total, so this means x+y = 10

Answer 40

if you have x liters of a 5% salt solution, you'll have 0.05x liters of pure salt

if you have y liters of a 25% salt solution, you'll have 0.25y liters of pure salt

in total, you'll have 0.05x+0.25y liters of pure salt

Answer 41

you want a final solution of 10 liters that is 10% salt

so you want 10*0.1 = 1 liter of pure salt

this means

0.05x+0.25y = 1

Answer 42

your two equations are

x+y = 10
0.05x+0.25y = 1

Answer 43

Okay let me solve that

Answer 44

alright

Answer 45

x = 7.5 and y = 2.5

Answer 46

getting the same

Answer 47

so you need

7.5 liters of the 5% salt solution

2.5 liters of the 25% salt solution

Answer 48

Yes that's it thank you so much ^-^ you have literally saved me lol

Answer 49

lol you did all the work really

Answer 50

but glad to be of help

Answer 51

I was panicking thinking I wouldn't be able to turn this in lol but thank you again

Answer 52

sure thing, and I'm glad things are clicking more

Answer 53

Yes it would be clicking better if I was more wide awake

Answer 54

good point, it's probably very late where you are

but it seems like you definitely know how to solve the systems...just getting the set up is what you need to work on

Answer 55

Yeah it's like almost midnight here and yeah I need to work on that I'm actually doing the last problem for this homework sheet ....kinda getting confused

Answer 56

ok where are you stuck?

Answer 57

Well I get that x is 10% and y would be 15% of commision and she invested 6,000

x = y = 6,000
0.10x + 0.15y = ?

Answer 58

sorry some of it was cut off

Answer 59

ok one sec

Answer 60

kk

Answer 61

let

x = total dollar amount of the rugs sold


Her commission on rugs is 10%, so if she makes x dollars on selling rugs, then she earns 0.10x dollars in commission from selling the rugs

Her commission on furniture is 15%, and she sells $12,500 worth of it. So she earns 0.15*12500 = 1875 dollars in commission from selling the furniture

In total, she earns 0.10x + 1875 dollars in commission from selling rugs and furniture

Answer 62

she wants to earn $6,000 in commission, so this means she wants

0.10x + 1875 = 6000

solve that for x to get your answer

Answer 63

x = 41,250

Answer 64

you got it

Answer 65

yay thanks you and for this problem the answer would be 1150 or 1100?

Answer 66

when you do linear regression, you get this approximate line

y = 20.225x - 39664

Answer 67

plug in x = 2012

y = 20.225x - 39664

y = 20.225(2012) - 39664

y = 1,028.7

so I'd say it's either 1000 or 1100

Answer 68

unfortunately this regression line both underestimates and overestimates values, so it's hard to say

Answer 69

oh okay I'll pick one but thank you you really helped me I'm going to go to bed Night

Answer 70

good night

Answer 71

:)