Question

Giuliana has 22 quarters and dollar coins worth a total of $10.75.

Answer 1

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.

Answer 2

Let

q------> the number of quarters coins

d------> the number of dollars coins

we know that

$1\ quarter=\ 0.25$

$q+d=22$

$q=22-d$ ------> equation A

$0.25q+d=10.75$ -----> equation B

substitute equation A in equation B

$0.25[22-d]+d=10.75$

therefore

the answer is the option

$0.25[22-d]+d=10.75$