Latest exam Aptitude Question SOLUTION: Jayne has 3 quarters, 2 dimes, a nickel, and 2 pennies in her pocket. How many different amounts of money can she make using some or all of her money?

I have the Teacher's edition of Prentice Hall Pre-Algebra. The Answer is 44. The book does not say how to get at it, but then, I tried and tried and this is what I did. I abreviated the coins' name andassigned a number to each coin, thus: Q1, Q2, Q3, D1, D2, N , P1 and P2. Then I did different orders until I got 44:
1=Q1
2=Q1 Q2
3= Q1 Q2 Q3
4= Q1 Q2 Q3 D1
5= Q1 Q2 Q3 D1 D2
6= Q1 Q2 Q3 D1 D2 N
7= Q1 Q2 Q3 D1 D2 N P1
8= Q1 Q2 Q3 D1 D2 N P1 P2
9=------Q2 Q3 D1 D2 N P1 P2
10= --------Q3 D1 D2 N P1 P2
11=--------------D1 D2 N P1 P2
12=-------------------D2 N P1 P2
13=------------------------N P1 P2
14=---------------------------P1 P2
15=-------------------------------P2
16= Q2
17= Q3
18= D1
19= D2
20= N
21= P1
22= P2
23= Q2 Q3
24= Q3 D1
25= D1 D2
26= D2 N
27= N P1
28= P1P2
29= P2 Q1
30= Q1 Q3
31= Q2 D1
32= Q3 D2
33= D1 N
34= D2 P1
35= N P2
36= Q1 D1
37= Q2 D2
38= Q3 N
39= D1 P1
40= D2 P2
41= Q1 D2
42= Q2 N
43= Q3 P1
44= d1 P2
BTW, I want to express to the editorial house PRENTICE HALL my frustration for throwing a problem this complex on a frigging PRE-ALGEBRA TEXTBOOK and then, just give the frigging answer''44'' without further explaining how one arrived to it. Talking about pedagogy! The TEAM responsible to put this question on the book really SUCK BIG TIME! If I had my way, I would FORBID all of YOU from writing any book EVER again!