Problema Solution
Nathaniel gave half his algebra problems to Charlie; Charlie then gives half of his algebra problems to Nathaniel. Nathaniel and Charlie repeat this two-step process twice more. If Nathaniel now has 37 algebra problems and Charlie has 19 algebra problems, with how many algebra problems did Charlie start?
Answer provided by our tutors
Charlie started with 40 problems and Nathaniel started with 16 problems.
Indeed:
Nathaniel gave half his algebra problems to Charlie:
(1/2)16 = 8 number of prob. Nathaniel has
40 + 8 = 48 number of prob. Charlie has
Charlie then gives half of his algebra problems to Nathaniel:
8 + 48/2 = 32 number of prob. Nathaniel has
48/2 = 24 number of prob. Charlie has
Nathaniel gave half his algebra problems to Charlie:
32/2 = 16 number of prob. Nathaniel has
24 + 16 = 40 number of prob. Charlie has
Charlie then gives half of his algebra problems to Nathaniel:
16 + 40/2 = 36 number of prob. Nathaniel has
40/2 = 20 number of prob. Charlie has
Nathaniel gave half his algebra problems to Charlie:
36/2 = 18 number of prob. Nathaniel has
20 + 18 = 38 number of prob. Charlie has
Charlie then gives half of his algebra problems to Nathaniel:
18 + 38/2 = 37 number of prob. Nathaniel has
38/2 = 19 number of prob. Charlie has