SOLUTION: the coins in a piggy bank are all dimes, nickles and quarters. there are twice as many dimes as quarters, and two more nickles than quarters. if the value of all the coins in the b

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Question 577355: the coins in a piggy bank are all dimes, nickles and quarters. there are twice as many dimes as quarters, and two more nickles than quarters. if the value of all the coins in the bank is $7.60, how many dimes are there?
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) +d+=+2q+
(2) +n+=+q+%2B+2+
(3) +5n+%2B+10d+%2B+25q+=+760+ ( in cents )
-------------------------
Substitute (10 and (2) into (3)
(3) +5%2A%28+q+%2B+2+%29+%2B+10%2A%282q%29+%2B+25q+=+760+
(3) +5q+%2B+10+%2B+20q+%2B+25q+=+760+
(3) +50q+=+760+-+10+
(3) +50q+=+750+
(3) +q+=+15+
and
(1) +d+=+2q+
(1) +d+=+2%2A15+
(1) +d+=+30+
and
(2) +n+=+q+%2B+2+
(2) +n+=+15+%2B+2+
(2) +n+=+17+
There are 30 dimes
check:
(3) +5n+%2B+10d+%2B+25q+=+760+
(3) +5%2A17+%2B+10%2A30+%2B+25%2A15+=+760+
(3) +85+%2B+300+%2B+375+=+760+
(3) +760+=+760+
OK