SOLUTION: Marysia has saved ​$48.75 in nickels and loonies. If she has 3 nickels fewer than three dash eighths the number of loonies​, how many coins of each type does Marysia​ have?

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Question 1137966: Marysia has saved ​$48.75 in nickels and loonies. If she has 3 nickels fewer than three dash eighths the number of loonies​, how many coins of each type does Marysia​ have?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of nickels
Let +k+ = the number of loonies
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(1) +n+=+%283%2F8%29%2Ak+-+3+
The value of a loonie is:
+48.75+-+5n+
(2) +k%2A%28+48.75+-+5n+%29+ is the value of +k+ loonies
------------------------------------------------------------
(1) +%283%2F8%29%2Ak+=+n+%2B+3+
(1) +k+=+%288%2F3%29%2A%28+n+%2B+3+%29+
and
(2) +%288%2F3%29%2A%28+n+%2B+3+%29+%2A%28+48.75+-+5n+%29+ is the value of +k+ loonies
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+5n+%2B+%288%2F3%29%2A%28+n+%2B+3+%29+%2A%28+48.75+-+5n+%29+=+48.75+
+15n+%2B+8%2A%28+n+%2B+3+%29%2A%28+48.75+-+5n+%29+=+3%2A48.75+
+15n+%2B+%28+8n+%2B+24+%29%2A%28+48.75+-+5n+%29+=+146.25+
+15n+%2B+390n+%2B+1170+-+40n%5E2+=+146.25+
+40n%5E2+-+405n+-+1023.75+=+0+
Solve with quadratic formula to find number of nickels
Then find number of loonies
There could be an easier way to do this. Get a 2nd opinion
and check my math.

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is clear from the condition, that the number of loonies must be multiple of 8: 8, or 16, or 24 and so on.


So, I will easily solve the problem by "trial and error" method.



    T       A       B       L       E  



Loonies, L   Nickels N = %2848.75-L%29%2F5       N = %283%2F8%29%2AL-3 
-------------------------------------------------------------------

   8	        815                         0                             
  16     	655	                    3                             
  24     	495	                    6                             
  32     	335	                    9
  40     	175	                   12
  48     	15	                   15    <<<---===  ANSWER
  56           -145	                   18
  64           -305	                   21


ANSWER.  48 loonies and 15 nickels.


Or, using equations 

    L + 0.05%2A%28%283%2F8%29%2AL-3%29 = 48.75


    8L + 0.05*(3L -24) = 48.75*8

    8.15L = 48.75*8 + 0.05*24

    L = %2848.75%2A8+%2B+0.05%2A24%29%2F8.15 = 48.


The same answer.

Solved.