SOLUTION: This is a system if equations word problem. "Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have?" I've tried this prob

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: This is a system if equations word problem. "Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have?" I've tried this prob      Log On


   



Question 833413: This is a system if equations word problem.
"Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have?"
I've tried this problem for over an hour and I just can't seem to get it. Thanks to anyone who can help! Could you please explain how you got the answer as well?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert dollar to cents
She has +4.5%2A100+=+450+ cents
Let +d+ = the number of dimes she has
Let +q+ = the number of quarters she has
-------------------
(1) +d+=+q+%2B+3+
(2) +10d+%2B+25q+=+450+
-----------------------
(1) +d+-+q+=+3+
Multiply both sides of (1) by +25+
and add (1) and (2)
(2) +10d+%2B+25q+=+450+
(1) +25d+-+25q+=+75+
+35d+=+525+
+d+=+15+
and, since
(1) +d+=+q+%2B+3+
(1) +15+=+q+%2B+3+
(1) +q+=+12+
She has 15 dimes and 12 quarters
check:
(2) +10d+%2B+25q+=+450+
(2) +10%2A15+%2B+25%2A12+=+450+
(2) +150+%2B+300+=+450+
(2) +450+=+450+
OK