BOTTLES AND CANS


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.

pc = 3qc

Quincy collected four times as many bottles as Rosa.

qb = 4rb

All collected the same number of items.

pc + pb = qc + qb = rc + rb

The three as a group had collected exactly as many cans as bottles.

qb + rb + pb = qc + rc +pc

 

Added together, the three collected fewer than 200 items in all.

pc + pb + qc + qb +rc + rb < 200

 

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