SOLUTION: Question: After closing down his lemonade stand, David finds that he has 3 and 1/2 times as many dimes as quarters. Their combined value is $15.60. How many dimes does he have?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Question: After closing down his lemonade stand, David finds that he has 3 and 1/2 times as many dimes as quarters. Their combined value is $15.60. How many dimes does he have?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 919186: Question: After closing down his lemonade stand, David finds that he has 3 and 1/2 times as many dimes as quarters. Their combined value is $15.60. How many dimes does he have?
This is the last question of my assignment and I have already done this question multiple times but I cannot seem to find the answer. I was told the answer was 91, but I do not understand how the answer came to be.
How is the answer 91?
Help would gladly be needed!
Found 3 solutions by stanbon, josmiceli, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Question: After closing down his lemonade stand, David finds that he has 3 and 1/2 times as many dimes as quarters. Their combined value is $15.60. How many dimes does he have?
-----
Equations:
Quantity:: d = 3.5q
Value:::: 10d + 25q = 1560 cents
--------------------------------------
Substitute for "d" and solve for "q"::
10*3.5q + 25q = 1560
35q + 25q = 1560
60q = 1560
q = 26 (# of quarters)
---
solve for "d"
d = 3.5q
d = 3.5*26 = 91 (# of dimes)
-----------------
Cheers,
Stan H.
=================

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = number of dimes he has
Let +q+ = number of quarters he has
----------------------------------
(1) +d+=+3.5q+
(2) +10d+%2B+25q+=+1560+ ( in cents )
-----------------------------------
By substitution:
(2) +10%2A3.5q+%2B+25q+=+1560+
(2) +35q+%2B+25q+=+1560+
(2) +60q+=+1560+
(2) +q+=+26+
---------------
and
(1) +d+=+3.5q+
(1) +d+=+3.5%2A26+
(1) +d+=+91+
----------------
There are 91 dimes
check:
(2) +10d+%2B+25q+=+1560+
(2) +10%2A91+%2B+25%2A26+=+1560+
(2) +910+%2B+650+=+1560+
(2) +1560+=+1560+
OK

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
After closing down his lemonade stand, David finds that he has 3 and 1/2 times as many dimes as quarters. Their combined value is $15.60. How many dimes does he have?
-------------
Each set of 3.5 dimes and 1 quarter = 60 cents
1560/60 = 26 sets
--> 91 dimes