Giuliana has 22 quarters and dollar coins worth a total of $10.75. which equation can be used to find d, the number of dollar coins giuliana has? d – 22 + 0.25d = 10.75 0.25d + 22 – d = 10.75 0.25(22 – d) + d = 10.75 d + 0.25(d – 22) = 10.75

Use the letters q and d to represent # of quarters and # of dollars.

q + d = 22 coins.

$0.25q + $1.00d = $10.75        Mult. this by 100 to eliminate fractions:
                                                 25q + 100d = 1075

Subst. q = 22 - d into the 2nd equation:

25 (22  - d) + 100 d = 1075

550 - 25d + 100d = 1075
550 + 75d = 1075
           75 d = 525
                 d = 7

q + d = 22, so if d = 7, then q = 22-7, or q=15.

There are 15 quarters and 7 dimes.