SOLUTION: Jane has nickles, dimes and quaters which total $1.90. She has twice as many quaters as dimes. She has 3 times as many quaters as nickels. How many quaters does she have.

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Jane has nickles, dimes and quaters which total $1.90. She has twice as many quaters as dimes. She has 3 times as many quaters as nickels. How many quaters does she have.      Log On

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Question 547270: Jane has nickles, dimes and quaters which total $1.90. She has twice as many quaters as dimes. She has 3 times as many quaters as nickels. How many quaters 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
given:
(1) +q+=+2d+
(2) +q+=+3n+
(3) +5n+%2B+10d+%2B+25q+=+190+ ( in cents )
--------------------------
From (1)
(1) +5q+=+10d+
(3) +5n+%2B+5q+%2B+25q+=+190+
and, from (2)
(2) +n+=+q%2F3+
(3) +%285%2F3%29%2Aq+%2B+5q+%2B+25q+=+190+
Multiply both sides by 3
(3) +5q+%2B+15q+%2B+75q+=+570+
(3) +95q+=+570+
(3) +q+=+6+
and
(1) +d+=+q%2F2+
(1) +d+=+3+
and
+n+=+q%2F3+
+n+=+2+
She has 2 nickels, 3 dimes, and 6 quarters
check answer:
(3) +5%2A2+%2B+10%2A3+%2B+25%2A6+=+190+
(3) +10+%2B+30+%2B+150+=+190+
(3) +190+=+190+
OK