Ask your own question, for FREE!
Mathematics 39 Online
OpenStudy (anonymous):

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)

OpenStudy (helder_edwin):

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

OpenStudy (helder_edwin):

agree?

OpenStudy (anonymous):

Yes

OpenStudy (helder_edwin):

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

OpenStudy (anonymous):

5 c

OpenStudy (helder_edwin):

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

OpenStudy (anonymous):

.10x+.05y=1.10

OpenStudy (helder_edwin):

YES! do u understand?

OpenStudy (anonymous):

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

OpenStudy (helder_edwin):

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

OpenStudy (helder_edwin):

no=now

OpenStudy (anonymous):

What would be the first step ?

OpenStudy (helder_edwin):

what do you think? what looks odd?

OpenStudy (anonymous):

Umm..... Idk

OpenStudy (helder_edwin):

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

OpenStudy (anonymous):

So what would I do first ?

OpenStudy (helder_edwin):

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)

OpenStudy (anonymous):

Is it 3 ?

OpenStudy (helder_edwin):

no! 100

OpenStudy (anonymous):

Ok so I multiply everything in the second equation by 100

OpenStudy (helder_edwin):

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

OpenStudy (anonymous):

So now I have 10x+5y =110

OpenStudy (helder_edwin):

what is your new second equation?

OpenStudy (helder_edwin):

YES!

OpenStudy (anonymous):

Ok so what would be the next step ?

OpenStudy (helder_edwin):

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

OpenStudy (anonymous):

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

OpenStudy (helder_edwin):

actually -10

OpenStudy (anonymous):

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

OpenStudy (helder_edwin):

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

OpenStudy (helder_edwin):

what next?

OpenStudy (anonymous):

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

OpenStudy (helder_edwin):

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

OpenStudy (anonymous):

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

OpenStudy (helder_edwin):

missed a sign!

OpenStudy (anonymous):

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

OpenStudy (anonymous):

I think

OpenStudy (helder_edwin):

YES (don't think BE SURE)

OpenStudy (helder_edwin):

what next?

OpenStudy (anonymous):

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

OpenStudy (helder_edwin):

you are right!

OpenStudy (helder_edwin):

GOOD JOB!

OpenStudy (anonymous):

Thanks a lot !

OpenStudy (helder_edwin):

u r welcome

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
danielfootball123: HAPPY EASTER!!!!
3 minutes ago 2 Replies 0 Medals
Puck: for all you amazing people
1 hour ago 2 Replies 2 Medals
Breathless: update on drawing.
10 minutes ago 12 Replies 5 Medals
ShadowKid3: what are examples of a class three lever?
1 day ago 3 Replies 2 Medals
alphaXtiger: Help pls
2 days ago 3 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!