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

Spreadsheet solution