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)
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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
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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
\[ \Large \begin{cases}
x+y=20\\ 0.10x+0.05y=1.10
\end{cases} \]
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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
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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
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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 ?
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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
\[ \Large \begin{cases}
-10x-10y=-200\\ 10x+5y=110
\end{cases} \]
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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!
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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 !
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