Question 18
Peter has $111$ red and $111$ blue marbles. Every day, Peter's uncle lets him exchange either $11$ red marbles for $7$ blue marbles or $20$ blue marbles for $28$ red marbles.
a. Can Peter increase the total number of marbles he has by $20$ after several exchanges?
b. Can Peter increase the total number of marbles he has by $33$ after several exchanges?
c. Can Peter ever have three times as many blue marbles as he has red ones?
a. Can Peter increase the total number of marbles he has by $20$ after several exchanges?
b. Can Peter increase the total number of marbles he has by $33$ after several exchanges?
c. Can Peter ever have three times as many blue marbles as he has red ones?