Joe has a collection of nickels and dimes that is worth $5.40. If the number of dimes were doubled and the number of nickels were increased by 10, the value of the coins would be $10.20. How many dimes does he have?

0.1dn+0.05n=5.4................1.

0.2d+(n+10)0.05=10.2.

0.2d+0.05n+0.5=10.2

0.2d+0.05n=9.7.....................2.

Multiply Equation 1 by 2 and by substraction from equation 2.

0.2d+0.1n=10.8.

0.2d+0.05n=9.7.

0.05n=1.1.'

n=1.1/0.05.

=22.

d=(9.7-0.05n)/0.2.

=(9.7-0.05*22)/0.2

=43.