SOLUTION: If I have 200 loonies and quartres and both the coins amount equal 91.25 how many of each coin do i have

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Question 947387: If I have 200 loonies and quartres and both the coins amount equal 91.25 how many of each coin do i have
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I guess your "loonies" are Canadian $1 coins. (I do not recall ever seeing one, but I have only visited Canada in very short trips).

IF YOU HAVE STUDIED SYSTEMS OF LINEAR EQUATIONS:
x= number of loonies
y= number of quarters
"I have 200 loonies and quarters" translates as
x%2By=200 .
Since
x= value of x loonies in Canadian dollars, and
0.25y=y%2F4= value of y quarters in Canadian dollars,
if the total of both types of coins amounts to 91.25,
x%2B0.25y=91.25 or x%2By%2F4=91.25 .
We can turn that equation into a prettier equivalent equation
by multiplying both sides of the equal sin times to get
4%28x%2B0.25y%29=4%2A91.25<--->4x%2By=365

Now we have
system%28x%2By=200%2C4x%2By=365%29-->system%28y=200-x%2C4x%2By=365%29-->system%28y=200-x%2C4x%2B200-x=365%29-->system%28y=200-x%2C3x%2B200=365%29-->system%28y=200-x%2C3x=365-200%29-->system%28y=200-x%2C3x=165%29-->system%28y=200-x%2Cx=165%2F3%29-->system%28y=200-x%2Cx=55%29-->system%28y=200-55%2Cx=55%29-->highlight%28system%28y=145%2Cx=55%29%29

IF YOU HAVE NOT STUDIED SYSTEMS OF LINEAR EQUATIONS:
x= number of loonies
"I have 200 loonies and quarters" translates as
200-x= number of quarters.
Since
x= value of x loonies in Canadian dollars, and
0.25%28200-x%29= value of 200-x quarters in Canadian dollars,
if the total of both types of coins amounts to 91.25,
x%2B0.25%28200-x%29=91.25 .
Then,
x%2B0.25%28200-x%29=91.25-->x%2B50-0.25x=91.25-->x-0.25x%2B50=91.25-->x%281-0.25%29%2B50=91.25-->0.75x%2B50=91.25-->0.75x=91.25-50-->0.75x=41.25-->x=41.25%2F0.75-->highlight%28x=55%29,
and 200-x=200-55-->200-x=highlight%28145%29 .

Either way, you have highlight%2855%29 loonies and highlight%28145%29 quarters.