Answer :
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
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
[tex]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.[/tex]