maths question

Let x be the number of 10 notes, y be the number of 20 notes and z be the number of 50 notes he has.

(The number of $20-notes is less than that of 10 notes by 5)
y = x﹣5 ---(1)

(The number of $50-notes is more than half of the number of 20 notes by 7)
z = y/2 + 7 ---(2)

(David has 22 banknotes altogether)
x + y + z = 22 ---(3)

Substitute (1) to (2),
z = y/2 + 7
= (x﹣5)/2 + 7
= x/2﹣5/2 + 7
= x/2 + 9/2 ---(4)

Substitute (1) and (4) to (3).
x + (x﹣5) + (x/2 + 9/2) = 22
2x﹣5 + x/2 + 9/2 = 22
Multiply both sides by 2
4x﹣10 + x + 9 = 44
5x = 45
x = 9
put it into (1),
y = x﹣5
= 9﹣5
= 4 ---(5)
Substitute (5) to (4),
z = x/2 + 9/2
= 9/2 + 9/2
= 9

∴x = 9, y = 4, z = 9.
∴David has 9 $10 notes, 4 $20 notes and 9 $50 notes in his wallet.

Let no of 10 notes=A
no of 20 notes=B
no of 50 notes=C
A=B+5
C=B/2+7
A+B+C=22
i.e. B+5+B+B/2+7=22
2B+B/2+12=22
2B+B/2=10
4B/2+B/2=10
5B/2=10
5B=10*2
5B=20
B=20/5
=4
A=B+5
=4+5
=9
C=B/2+7
=4/2+7
=9

2007-12-28 13:13:14 補充：
A=9B=4C=9