<PRE><B>Question 342568</B>
Your piggy bank contains $19.75 in dimes and quarters.
 There are 100 coins in all. How many dimes are there? 
:
Let d = no. of dimes
Let q = no. of quarters
:
$total equation
.10d + .25q = 19.75
:
No. of coins equation
d + q = 100
d = (100-q)
:
Replace d with (100-q) in the $total equation
.10(100-q) + .25q = 19.75
10 - .10q + .25q = 19.75
.15q = 19.75 - 10
.15q = 9.75
q = {{{9.75/.15}}}
q = 65 quarters
then
100 - 65 = 35 dimes
;
:
Check solution in the $total equation
.10(35) + .25(65) = 
3.50 + 16.25 = 19.75, confirms our solutions</PRE>