SOLUTION: Mary has a jar with one-dollar bills, half-dollar coins, and quarters valuing $14.00. She has twice as many quarters than she does half-dollar coins and the same amount of half-dol

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Question 1026149: Mary has a jar with one-dollar bills, half-dollar coins, and quarters valuing $14.00. She has twice as many quarters than she does half-dollar coins and the same amount of half-dollar coins as one-dollar bills. How many of each does she have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = number of $1 bills
Let +h+ = number of half dollar coins
Let +q+ = number of quarters
----------------------------
(1) +q+=+2h+
(2) +h+=+b+
(3) +1%2Ab+%2B+.5%2Ah+%2B+.25q+=+14+
---------------------------
(3) +100b+%2B+50h+%2B+25q+=+1400+
(3) +4b+%2B+2h+%2B+q+=+56+
Substitute (1) and (2) into (3)
(3) +4%2Ah+%2B+2%2Ah+%2B+2%2Ah+=+56+
(3) +8h+=+56+
(3) +h+=+7+
and
(2) +h+=+b+
(2) +b+=+7+
and
(1) +q+=+2h+
(1) +q+=+2%2A7+
(1) +q+=+14+
---------------
She has
7 $1 bills
7 half dollar coins
14 quarters
--------------
check:
(3) +1%2Ab+%2B+.5%2Ah+%2B+.25q+=+14+
(3) +1%2A7+%2B+.5%2A7+%2B+.25%2A14+=+14+
(3) +7+%2B+3.5+%2B+3.5+=+14+
(3) +14+=+14+
OK