Word problem has me stumped

[Shoy00]

Hi
My son has a word problem that I can't solve. Can you help me with a solution?

Gregory, Samantha and Pedro go to the mall. Gregory and Samantha spend $17 dollars in total. Samantha and Pedro spend $20 in total. Gregory and Pedro spend $21 in total. How much money does each person spend?

Can you please show your work? I'm completely stumped. Thanks.

[Math Tutor]

Suppose
Gregory spent x dollars
Samantha spent y dollars and
Pedro spent z dollars

x + y = 17 => x = 17 -y
y + z = 20 => z = 20 - y
x + z = 21


x + z = 21
(17 - y) + (20 - y) = 21
17 - y + 20 - y = 21
-2y = 21 - 20 - 17
-2y = -16
so y = 8 or Samantha spent $8

Gregory spent x = 17 - y <=> x = 17 - 8 <=> x = 9
Gregory spent $9

How much spent Pedro ?

[Edward]

Let's Gregory is G, Samanta is S and Pedro is P
G+S=17;
S+P=20;
G+P=21

then

(G+S)+(S+P)+(G+P)=17+20+21

2G+2S+2P=58;

2(G+S+P)=58 and

G+S+P=29

G+S=17 and G+S+P=29; 17+P=29 P=12

S+P=20 and G+S+P=29; G+20=29 G=9

G+P=21 and G+S+P=29; S+21=29; S=8

[Math Tutor]

Edward,
this is a perfect solution.
Thank you!