Question

easy pizy! I have 10 cents and 5 cents coins. there are 40 coins in total how many 5 cents are and how many 10 cents do I have in the cup?

Answer 1

you need to know how much money (total cents) are in the cup. otherwise, we could say you have 40 nickels and no dimes, for example.

Answer 2

ok they are aking me to set an equation and from that equation I have to figure out how many coins of 5 cents are and how many coins of 10 cents are.

Answer 3

Yes, but they have to tell you how much money the coins add up to.

Answer 4

Have this individual grab a handful of coins making sure there are only two types of coins in the group (i.e., nickels and dimes, quarters and pennies, pennies and dimes, etc).l your friend should tell you the type of coins they’ve chosen, how many coins they have and the dollar amount of the group. From this information, you will set up two sets of equations and determine how many of each coin they have in their hand.

Answer 5

this is what they ask me

Answer 6

read carefully
l your friend should tell you the type of coins they’ve chosen, how many coins they have and the dollar amount of the group.

Answer 7

I have here nickels and dimes
in total there are 40

Answer 8

and the dollar amount of the group.

Answer 9

in dimes there are 1.30$ and in nickels are 1.35

Answer 10

in total there are 2.65
and here is what I have done so far
0.10+0.052.65
d+n=40c

Answer 11

Well, I would not tell the person that, because they could divide 130 by 10 to get 13 dimes
and 135/20 to get 27 nickels

Just tell how much the dimes and nickels add up to: $2.65 that makes it harder to figure out

Answer 12

oh ok :)... so what I have done so far is right?

Answer 13

0.10+0.052.65<-- this one is not an equation
d+n=40c (what is c? just d+n= 40 makes sense)

Answer 14

amount of coins

Answer 15

oh ok

Answer 16

now there I dont know what else to do

Answer 17

if you had d dimes, how much money is that? I would say d*0.10
(the number of dimes times 10 cents per dime)
so your first equation should show that the dimes and nickels add up to 2.65

Answer 18

so lets say
0.10d+0.05n=2.65

Answer 19

and after that ?? :?

Answer 20

yes, you now have 2 equations and 2 unknowns
0.10d+0.05n=2.65
d+n= 40

now you can solve (though you already know the answer!)
I would multiply the top equation by 100 to get rid of the decimals
(multiply both sides, every term by 100)

you get
10d + 5n = 265
d +n = 40

you can do a number of things next. one way is multiply the bottom equation by -5
(every term, both sides)
then add the equations, and solve for d

Answer 21

it gives me 26

Answer 22

265-5=260
260/10=26

Answer 23

no, you are doing something wrong. Start with
10d + 5n = 265
d +n = 40

multiply the bottom equation by -5. what do you get? write down the new equation

Answer 24

40*-5=200

Answer 25

-200

Answer 26

d +n = 40
write down -5* in front of every term

Answer 27

d+n=-200

Answer 28

?

Answer 29

-5d+5n=-200

Answer 30

d +n = 40
write down -5* in front of every term

we multiply both sides of the equation (to be fair!)

-5*(d+n)= 40* -5
now distribute the -5

Answer 31

closer by -5*n is -5n, don't you agree?

Answer 32

yes

Answer 33

so both are negative

Answer 34

-5d+-5n=-200

Answer 35

so you now have
10d + 5n = 265
-5d - 5n = -200

add the equations: write down the left sides added together = the right side added together

Answer 36

like this
10d -5d + 5n -5n= 265-200

Answer 37

simplify: you have 10 d's and you take away 5 d's. how many d's are left?
you have 5 n's and take away 5 n's. how many n's do you have
and 265-200 is 65
what do we have for the new equation?

Answer 38

how did you get265?

Answer 39

We had the equation
0.10d+0.05n=2.65
I don't like decimals, so I multiplied both sides of the equation by 100

you get
100*(0.10d + 0.05n)= 2.65*100
distribute the 100:

100*0.10d + 100*0.05n = 265
10d+5n= 265
follow?

Answer 40

yes

Answer 41

so we have
10d + 5n = 265
d +n = 40

then we multiply the bottom equation by -5 (because we want the n's to go away)
we get

10d + 5n = 265
-5d -5n = -200

now add the 2 equations. do you know how to do that?

Answer 42

like @phi said 10d -5d + 5n -5n= 265-200

Answer 43

yes, but now simplify it by combining "like terms"

Answer 44

5d+0n=65?

Answer 45

yes. and of course 0*n is 0 and 5d+0 is just 5d
so you have
5d= 64

divide both sides by 5 to find d

Answer 46

*65 not 64

Answer 47

correct sorry

Answer 48

sorry? I made the typo not you

Answer 49

64/5=12.8 or 13

Answer 50

is 65

Answer 51

It's 65/5 ( I mistyped)

Answer 52

:)

Answer 53

hehe it ok , I made a mistake too

Answer 54

so is 13

Answer 55

and for the nickels dont I have to do another equation?

Answer 56

yes, now use one of the 2 equations we started with to find n.
Choose the easiest one. in this case
d+n= 40

Answer 57

ok

Answer 58

replace d with 13:
13+n= 40
add -13 to both sides to find n

Answer 59

18?

Answer 60

wait from 40 sorry

Answer 61

is going to be n=27

Answer 62

adding -13 is the same as subtracting 13. But for me, it is less confusing to always add, and if I want to make something 0 (like +13) I just add -13

Answer 63

yes d= 13 and n=27, which are the numbers you picked in the first place.

I hope all this make sense.

Answer 64

hehe yes it does ...Thank you so so so much for helping me! ;)

Answer 65

If you want more info, here is a video that is helpful
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/solving-systems-by-elimination

Answer 66

Ok thank you1, I will watch that video :)