SOLUTION: A group of nickels, dimes, and quarters is worth $9.50. There are two-thirds as many nickels as dimes and half as many dimes as quarters. How many quarters are there?

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Question 266429: A group of nickels, dimes, and quarters is worth $9.50. There are two-thirds as many nickels as dimes and half as many dimes as quarters. How many quarters are there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
n = number of nickels
d = number of dimes
q = number of quarters
given:
(1) 5n+%2B+10d+%2B+25q+=+950 (in cents)
(2) n+=+%282%2F3%29%2Ad
(3) d+=+%281%2F2%29%2Aq
-----------------
From (3)
q+=+2d
By substitution:
(1) 5%2A%282%2F3%29%2Ad+%2B+10d+%2B+25%2A%282d%29+=+950
%2810%2F3%29%2Ad+%2B+10d+%2B+50d+=+950
10d+%2B+30d+%2B+150d+=+2850
190d+=+2850
d+=+15
From (3)
q+=+2d
q+=+30
There are 30 quarters
check answer:
(2) n+=+%282%2F3%29%2Ad
n+=+%282%2F3%29%2A15
n+=+10
and
(1) 5n+%2B+10d+%2B+25q+=+950
(1) 5%2A10+%2B+10%2A15+%2B+25%2A30+=+950
50+%2B+150+%2B+750+=+950
950+=+950
OK