Mike has 26 coins in his pocket, all dimes and quarters. If the coins are worth a total of $5.30, how many of each type of coin does he have

Let  d  =  number of dimes

Let  q  =  number of quarters

Number equation:  d + q  =  26

Value equation:  0.10d + 0.25q  =  5.30

Simplifying the value equation by multiplying by 100:  10d + 25q  =  530.

Solving the two equations:

   d + q  +  26   --->   multipling by -10   --->    -10d - 10q  =  -260

 10d + 25q  =  530                                --->     10d + 25q  =  530

Adding down the columns:                                          15q  =  270

                                                            --->                 q  =  18

                                        d + q  =  26   --->                d  =  8