Assign variables
LET qc = No. of cans QUINCY collected
LET pc = No. of cans PENNY collected
LET rc = No. of cans ROSA collected
LET qb = No. of bottles QUINCY collected
LET pb = No. of bottles PENNY collected
LET rb = No. of bottles ROSA collected
Translate words to equations
Penny collected three times as many cans as Quincy.
Quincy collected four times as many bottles as Rosa.
All collected the same number of items.
The three as a group had collected exactly as many cans as bottles.
Added together, the three collected fewer than 200 items in all.
Transforming the equations
pc = 3qc
qb = 4rb
Gives us qb + qc = 1/3 pc + 4 rb
Substitution
pc + pb = 1/3 pc + 4 rb = rc + rb