P6 Math Heuristic - Work Backwards (Answer)

Cass and Slide played a game of marbles. After the first game, Cass lost 3/5 of his marbles to Slide. After the second game, Slide lost 2/3 of his new total marbles to Cass. At the end of the two games, Cass had 8z marbles and Slide had 3z marbles.

a) How many marbles did Cass have at first? Give the answer in terms of z.

b) What were the total number of marbles they had when z = 35?

 

a)     Working backwards: Slide lost 2/3 of his marbles so he has 1/3 left. Undoing his loss in the second game,

1/3 = 3z

3/3 = 9z (Slide’s marbles at the beginning of second game)

Slide’s loss = 6z marbles

Undoing Cass’s win: 8z – 6z = 2z (Cass’s marbles at the beginning of second game)

Next, undoing Cass’s loss in the first game: (1 – 3/5) = 2/5 of his marbles left after the first game.

2/5 = 2z

5/5 = 2/2 x 5 = 5z (Cass’s marbles at first before the first game) [Answer]

 

b)     Total between Cass and Slide = 9z + 2z OR 8z + 3z = 11z (total unchanged)

If z = 35, total number of marbles = 11 x 35 = 385 [Answer]