Given :

The number of coins she have is 30 consisting of dimes and quarters. Total of

the coins is $5.10

To find :

The number of coins of dimes and quarters. Let the number of dimes be x, and the number of quarters be y.

Total number of coins she have is 30 consisting of dimes and quarters.

\(x + y = 30\) .........(1)

Total number of coins is $5.10 convert into cents, that is 510 cents.

\(10 x + 25 y = 510\) ............(2)

Solve equation (1) for x in terms of y. \(x = 30 - y\)

Substitute \(30 - y\) for x in equation (2),

\(10 (30−y) + 25y\)

\(= 510 300 − 10y + 25 y\)

\(= 510 15 y = 210 y\)

\(= 14\)

Substitute \(y=14\) in equation (2),

\(x + 14 = 30\)

\(x = 16\)

Thus, the number of dimes is 16 and the number of quarters is 14.