Question 807325
First assign a variable for the no. of pebbles each had
t = Taylor's pebbles
m = Marco's
g = Gino's
:
Write an equation for each statement.
Taylor collected 3 times as many pebbles as Marco.
t = 3m
 Gina collected 21 fewer pebbles than Taylor.
g = t - 21
 They collected 427 pebbles altogether.
t + m + g = 147
:
How many pebbles did Gina collect? 
We want to get varibles g and m in terms of t, then we have only one variable to deal with. 
g = (t-21) so that one is OK,
 however
3m = t
divide both sides by 3
m = t/3
:
In the last equation, replace g with (t-21) and m with t/3
t + (t-21) + t/3 = 147
Get rid of the fraction, multiply by 3 and you have
3t + 3(t-21) + t = 3(147)
3t + 3t - 63 + t = 441
7t = 441 + 63
7t = 504
t = 504/7
t = 72 pebbles for Taylor
then 
m = 72/3
m = 24 pebbles for Marco
and 
g = 72 - 21
g = 51 pebbles for Gina
:
The last step is to check and see if:
72 + 24 + 51 = 147
:
:
This is a common method in solving these multi-variable equations, you can
see that it is pretty logical, if you follow each step. CK