SOLUTION: A newsboy collected $68.50 on his paper route one week. The collection consisted of nickels,dimes and quarters. If he had 70 more nickels than quarters and 20 more dimes than nicke

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Question 536826: A newsboy collected $68.50 on his paper route one week. The collection consisted of nickels,dimes and quarters. If he had 70 more nickels than quarters and 20 more dimes than nickels,how many of each kind of coin did he have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels
Let d = number of dimes
Let +q = number of quarters
given:
(1) +5n+%2B+10d+%2B+25q+=+6850+ ( in cents )
(2) +n+=+q+%2B+70+
(3) +d+=+n+%2B+20+
--------------
(2) +q+=+n+-+70+
Substitute (2) and (3) into (1)
(1) +5n+%2B+10%2A%28+n+%2B+20+%29+%2B+25%2A%28+n+-+70+%29+=+6850+
(1) +5n+%2B+10n+%2B+200+%2B+25n+-+1750+=+6850+
(1) +40n+%2B+200+-+1750+=+6850+
(1) +40n+=+8400+
(1) +n+=+210+
and, since
(3) +d+=+n+%2B+20+
(3) +d+=+230+
and
(2) +q+=+n+-+70+
(2) +q+=+210+-+70+
(2) +q+=+140+
He had 210 nickels, 230 dimes, and 140 quarters
check:
(1) +5%2A210+%2B+10%2A230+%2B+25%2A140+=+6850+
(1) +1050+%2B+2300+%2B+3500+=+6850+
(1) +6850+=+6850+
OK