Question

Jackie has a jar of 54 coins consisting of dimes and quarters. If she has a total of $10.05, how many dimes does she have?

Answer 1

uhh..23 maybe?

Answer 2

wait no..

Answer 3

how are you trying to set up the problem?

Answer 4

31?

Answer 5

or were you just guessing?

Answer 6

messing around with it in my graphing calculator

Answer 7

ive done several different things and gotten 23 and 31

Answer 8

well I can't help you with your graphing calculator
I can help you with the math though, which is the important part.

Answer 9

alright im listening

Answer 10

help please

Answer 11

you can make a set of two equations out of this
let x=#dimes
let y=#quarters

Answer 12

"Jackie has a jar of 54 coins consisting of dimes and quarters"
we can interpret this mathematically as\[x+y=54\]making sense?

Answer 13

yes so far

Answer 14

now can you come up with an expression for how much money there is total in terms of x and y ?

Answer 15

x+y=$10.05

Answer 16

not quite...
You will need coefficients for this one that relate to the value of each coin.
For instance, if I have x quarters, then the amount of money I have in quarters is 0.25x (in dollars)
So here we have quarters \(and\) dimes adding to a total of $10.05
So what will the expression be?

Answer 17

.25x+.10y=10.05

Answer 18

good :)

Answer 19

this isnt so much what i had trouble with

Answer 20

i tried several different formulas and got several answers which i think are right lol.

Answer 21

it would help me alot if you could explain the use of the correct formula

Answer 22

the point is that now we have two equations with two variables, which can be solved in a number of ways
\[x+y=54\]\[0.25x+0.1y=10.05\]I recommend the first step is to get rid of the decimals in the second equation
can you do that?

Answer 23

normally to get rid of a variable you divide. its been awhile since i did this i forgot mutliple variables

Answer 24

I didn't say get rid of a variable, I said get rid or the decimals in the second equation

Answer 25

i apreciate the help by the way :)

Answer 26

you're welcome :)

Answer 27

um..

Answer 28

-.25?

Answer 29

and .10?

Answer 30

that seems ridiculous to me

Answer 31

what would happen if you multiplied both sides by 100 in the second equation?

Answer 32

ahh

Answer 33

haha

Answer 34

right, now it get's pretty easy pretty fast

Answer 35

totally forgot about doing that

Answer 36

yea lol

Answer 37

ok, so what is the second equation after multiplying by 100 ?

Answer 38

25x +10y = 10.05

Answer 39

not exactly
I think you forgot to multiply \(both\) sides

Answer 40

1005 :)

Answer 41

= 1005 soryr

Answer 42

does moderator mean your employed by this site or just an admin?

Answer 43

right, so now our system is\[x+y=54\]\[25x+10y=1005\]now I would prescribe the substitution method from here

Answer 44

I'm just a moderator, which basically means I deal with immature trolls and such
I also try to contribute ideas to administration

Answer 45

cool, did you start out as a user ?

Answer 46

yup, only been a mod for a couple weeks actually.
anyhow... do you know how to solve systems?

Answer 47

ya one sec, i think i have the anser

Answer 48

you used a computer lol

Answer 49

..or are you doing it by hand?

Answer 50

hand

Answer 51

i messed up tho

Answer 52

good :)
that is a consequence, but the practice is important

Answer 53

lol

Answer 54

it's easy to mess up with systems like this before you learn linear algebra
anyhow, what sub did you make?
can you show me what you did?

Answer 55

linear algebra?

Answer 56

is that tought in algebra 1 or 2

Answer 57

nevermind... higher math

Answer 58

its actually sad but ive taken agebra 1, 2, advanced with financial app and advanced geo

Answer 59

no it deals with matrices and such... it's usually around when you take calculus

Answer 60

the worst part is i slacked hard and didnt bother to atcually LEARN the work...just got as many correct asnwers asap

Answer 61

ah ok

Answer 62

anyway

Answer 63

whats the next step

Answer 64

o wait

Answer 65

can you do it normally?

Answer 66

-10y?

Answer 67

etc?

Answer 68

25x + 10y + -10y = 1005 + -10y

Answer 69

if you did that couldnt you combine like terms and then solve?

Answer 70

yeah, we used to contribute to that
they made me a mod partially to stop that habit and start teaching more

we have equation that we can name\[1)x+y=54\]\[2)25x+10y=1005\]and what you are doing would work if your "etc." is right, but you are doing it the hard way

you cannot combine like terms and solve yet because you still have both an x and a y

Answer 71

x = 40.2 - 0.4y thats the answer but i dont know how to convert to just one number

Answer 72

i think?

Answer 73

if not that way then i dont know

Answer 74

I'm showing you, please try to be patient I'm typing it out

Answer 75

and yea, open study used to be alot more pure answers instead of breaking it down

Answer 76

sorry, i was just elaborating lol

Answer 77

\[1)x+y=54\]\[2)25x+10y=1005\]we can turn equation 1) around and solve it for y\[y=54-x\]now we can substitute this expression in for \(y\) in equation 2) and it will only contain x's, which means we can then solve for x
what do you get by subbing \(y=54-x\) into equation 2)
???

Answer 78

25x+540=1005

Answer 79

1005 - 540 = 456

Answer 80

465*

Answer 81

thank you :)

Answer 82

?
you lost art of the expression
there should be another x term

Answer 83

*part of the...

Answer 84

hmm?

Answer 85

i got 18

Answer 86

\(y=54-x\)
subbing that into \[25x+10y=1005\]gives\[25x+10(54-x)=1005\]

Answer 87

let number of dimes be x
therefore quarters would be 54-x

0.1x + 0.25(54-x) = 10.05

now solve for x

Answer 88

what x= I don't yet know, I haven't checked

Answer 89

I am just prescribing the approach

Answer 90

now im confused again lol

Answer 91

why would you add another x into the equation

Answer 92

@sheg yes you are right, I was going to do elimination so I multiplied the other one first

Answer 93

though both give the same answer of course

Answer 94

@rkasser that is what we got by solving equaiton 1) for y
as I explained above

Answer 95

hey rkasser total number of coins = 54
and if out of 54 coins x are dimes so how many are left??/
it should be somewhat 54-x

Answer 96

@sheg I have said this already, please read above

Answer 97

So number of dimes = x
number of quarters = 54-x