Question

If your friend has 20 coins in his hand made up of dimes and nickels that equals $1.10 .How can you make two equations to show exactly how many of each coin he/she has in their hand ?(Show your work)

Answer 1

say x is the number of dimes
y the number of nickels
so
\[ x+y=20 \]

Answer 2

agree?

Answer 3

Yes

Answer 4

now. i know a dime is 10 c, right?
but what is a nickel?

Answer 5

5 c

Answer 6

then
\[ \Large 0.10x+0.05y=? \]

Answer 7

.10x+.05y=1.10

Answer 8

YES!
do u understand?

Answer 9

Yes I understand how I got the equation , but I'm not sure how to solve it .

Answer 10

you have no the system
\[ \Large \begin{cases}
x+y=20\\ 0.10x+0.05y=1.10
\end{cases} \]

Answer 11

no=now

Answer 12

What would be the first step ?

Answer 13

what do you think? what looks odd?

Answer 14

Umm..... Idk

Answer 15

the coefficients the first equation has integers, but the second has decimals

Answer 16

So what would I do first ?

Answer 17

have the coeficients of the same type of number!
by how much do u multiply the second eq? (count the number of decimals for a clue, it isn't 2)

Answer 18

Is it 3 ?

Answer 19

no!
100

Answer 20

Ok so I multiply everything in the second equation by 100

Answer 21

yes!
when you solve a system you think in an equation as a whole

Answer 22

So now I have 10x+5y =110

Answer 23

what is your new second equation?

Answer 24

YES!

Answer 25

Ok so what would be the next step ?

Answer 26

can you isolate on of the variables of both equations? say x

Answer 27

Would I have to multiply everything in the first equation by 10 ?

Answer 28

actually -10

Answer 29

So would it be -10x-10y=-200 ?

Answer 30

so you get the system
\[ \Large \begin{cases}
-10x-10y=-200\\ 10x+5y=110
\end{cases} \]

Answer 31

what next?

Answer 32

The x cancels out leaving me with -10y=-200 and 5y=110 correct ?

Answer 33

no!
you have to add the equations in order to have x canceled out!

Answer 34

Ok so does it leave me with -5y=90 ?

Answer 35

missed a sign!

Answer 36

-5y=-90 Then I divide both sides by -5 so y=18.

Answer 37

I think

Answer 38

YES (don't think BE SURE)

Answer 39

what next?

Answer 40

Umm....I thought we had the answer now 18 nickels and two dimes !

Answer 41

you are right!

Answer 42

GOOD JOB!

Answer 43

Thanks a lot !

Answer 44

u r welcome