Question

sally has 20 coins in her piggy bank,all dimes and quarters. The total amount of money is $3.05. How many of each coin does she have?

Answer 1

$x-\ amount\ of\ dimes\\\\y-\ amount\ of\ quarters\\\\ \left \{ {{x+y=20} \atop {0,1x+0,25y=3,05\ \ |*(-10)}} \right.\\\\ \left \{ {{x+y=20} \atop {-x-2,5y=-30,5}} \right. \\+-----\\Addition\\\\ -1,5y=-10,5\ \ \ | divide\ by\ -1,5\\\\ y=7\\\\x=13\\\\There\ are\ 7\ quarters\ and\ 13\ dimes.$

Answer 2

Let d = number of dimes, q = number of quarters 

Sally has 20 coins in her piggy bank, so 
d + q = 20 

The total amount of money is $3.05. 
Use the value of each coin multiplied by its number to get total value 
.10d + .25q = 3.05 
multiply everything by 100 to clear the decimal places 
10d + 25q = 305 and 
d + q = 20 

solve the second equation above in terms of either d or q - lets do d 
d = 20 - q 
sub that into the first equation 
10d + 25q = 305 
10(20 - q) + 25q = 305 
200 - 10q + 25q = 305 
15q = 105 
q = 105/15 = 7 
and from above 
d = 20 - q = 20 - 7 = 13 

so, there are 13 dimes and 7 quarters 
verify with orig problem 
13 + 7 = 20, OK, and $1.30 + $1.75 = $3.05