SOLUTION: A sum of rs 8400 is made up of 50,20,10 and 5 rupee notes. The number of 10 rupee note is five times the number of 5 rupee notes,four times the number of 20 rupee note and ten time

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A sum of rs 8400 is made up of 50,20,10 and 5 rupee notes. The number of 10 rupee note is five times the number of 5 rupee notes,four times the number of 20 rupee note and ten time      Log On


   

Question 937628: A sum of rs 8400 is made up of 50,20,10 and 5 rupee notes. The number of 10 rupee note is five times the number of 5 rupee notes,four times the number of 20 rupee note and ten times the number of 50 rupee note. what is the number of notes in each denomination
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 5 rupee notes
Let +b+ = number of 10 rupee notes
Let +c+ = number of 20 rupee notes
Let +d+ = number of 50 rupee notes
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(1) +b+=+5a+
(2) +b+=+4c+
(3) +b+=+10d+
(4) +5a+%2B+10b+%2B+20c+%2B+50d+=+8400+
-----------------------------------
(1) +a+=+b%2F5+
(2) +c+=+b%2F4+
(3) +d+=+b%2F10+
By substitution:
(4) +5%2A%28b%2F5%29+%2B+10b+%2B+20%2A%28b%2F4%29+%2B+50%2A%28b%2F10%29+=+8400+
Multiply both sides by +20+
(4) +20b+%2B+200b+%2B+100b+%2B+100b+=+168000+
(4) +420b+=+168000+
(4) +b+=+400+
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(1) +a+=+400%2F5+
(1) +a+=+80+
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(2) +c+=+400%2F4+
(2) +c+=+100+
-------------------
(3) +d+=+400%2F10+
(3) +d+=+40+
-------------------
There are:
80 of the 5 rupee notes
400 of the 10 rupee notes
100 of the 20 rupee notes
40 of the 50 rupee notes
----------------------
check:
(4) +5a+%2B+10b+%2B+20c+%2B+50d+=+8400+
(4) +5%2A80+%2B+10%2A400+%2B+20%2A100+%2B+50%2A40+=+8400+
(4) +400+%2B+4000+%2B+2000+%2B+2000+=+8400+
(4) +8400+=+8400+
OK