SOLUTION: marnie has 18 coins in the ratio of 1 dollar and 2 quarter. what coins does she spend to give a new ratio of dollars to quarters of 1:3? Give all possible answers.

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: marnie has 18 coins in the ratio of 1 dollar and 2 quarter. what coins does she spend to give a new ratio of dollars to quarters of 1:3? Give all possible answers.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1029239: marnie has 18 coins in the ratio of 1 dollar and 2 quarter. what coins does she spend to give a new ratio of dollars to quarters of 1:3? Give all possible answers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are twice as many quarters as dollars
Let +d+ = number of dollars
+d+%2B+2d+=+18+
+3d+=+18+
+d+=+6+
There are +18+-+6+=+12+ quarters
-------------
The only way to spend and get the ratio
+d%2Fq+=+1%2F2+ down to +d%2Fq+=+1%2F3+
is to spend dollars or both dollars and quarters
------------------
I can say:
+%28+6+-+x+%29+%2F+12+=+1%2F3+
Multiply both sides by +12+
+6+-+x+=+4+
+x+=+2+
Spend just 2 dollars
----------------------
Now I can say:
+%28+6+-+x+%29+%2F+%28+12+-+y+%29+=+1%2F3+
+3%2A%28+6+-+x+%29+=+12+-+y+
+18+-+3x+=+12+-+y+
+3x+-+y+=+6+
Any whole number solution is good as
long as +x+%3C+6+ and +y+%3C+12+
------------------
+x+=+4+ and
+y+=+6+ works
spend 4 dollars and 6 quarters
d/q = 2/6
-----------------------------
+x+=+5+ and
+y+=+9+ works
spend 5 dollars and 9 quarters
d/q = 1/3
------------------------------
+x+=+3+ and
+y+=+3+ works
spend 3 dollars and 3 quarters
d/q = 3/9
------------------------------
I think that's it