SOLUTION: Molly has 14.90 coins. she has two more nickels than dimes. she has eight fewer quarters than dimes. how many quarters does she have?

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Question 913545: Molly has 14.90 coins. she has two more nickels than dimes. she has eight fewer quarters than dimes. how many quarters does she 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
-----------------------------
(1) +5n+%2B+10d+%2B+25q+=+1490+ ( in cents )
(2) +n+=+d+%2B+2+
(3) +q+=+d+-+8+
----------------
There are 3 equations and 3 unknowns
so it's solvable
Substitute (2) and (3) into (1)
(1) +5%2A%28+d%2B2+%29+%2B+10d+%2B+25%2A%28+d+-+8+%29+=+1490+
(1) +5d+%2B+10+%2B+10d+%2B+25d+-+200+=+1490+
(1) +40d+=+1490+%2B+190++
(1) +40d+=+1680+
(1) +d+=+42+
and
(3) +q+=+d+-+8+
(3) +q+=+42+-+8+
(3) +q+=+34+
----------------
She has 34 quarters
check:
(2) +n+=+d+%2B+2+
(2) +n+=+42+%2B+2+
(2) +n+=+44+
---------------
(1) +5%2A44+%2B+10%2A42+%2B+25%2A34+=+1490+
(1) +220+%2B+420+%2B+850+=+1490+
(1) +1490+=+1490+
OK