SOLUTION: I have a math problem that say this: Constance has $2.80 in quarters and dimes. The number of quarters exceeds three times the number of dimes by 1. Find the number she has of each

Algebra ->  Equations -> SOLUTION: I have a math problem that say this: Constance has $2.80 in quarters and dimes. The number of quarters exceeds three times the number of dimes by 1. Find the number she has of each      Log On


   

Question 533419: I have a math problem that say this: Constance has $2.80 in quarters and dimes. The number of quarters exceeds three times the number of dimes by 1. Find the number she has of each kind. What do they mean by 1?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
They mean that she has 3 times as many quarters as dimes
plus 1 more quarter.
For example, if she had 5 dimes, then she would have
+3%2A5+ = 15 quarters plus 1 more quarter = 16 quarters
----------------
As for your problem,
Let q = number of quarters she has
Let d = number of dimes she has
given:
(1) +q+=+3d+%2B+1+
(2) +25q+%2B+10d+=+280+ ( in cents )
---------------------
Divide both sides of (2) by 5
(2) +5q+%2B+2d+=+56+
Substitute (1) into (2)
(2) +5%2A%28+3d+%2B+1+%29+%2B+2d+=+56+
(2) +15d+%2B+5+%2B+2d+=+56+
(2) +17d+=+51+
(2) +d+=+3+
and, since
(1) +q+=+3d+%2B+1+
(1) +q+=+3%2A3+%2B+1+
(1) +q+=+10+
She has 10 quarters and 3 dimes