Problema Solution
a boy puts the same number of penniesneach week into a money box. the weekly amount is more than one penny and the box startes empty. after a few weeks there was a total of 65p in the box, an a few weeks later there was a total of £1.04. How many pennies does he put into the box each week?
Answer provided by our tutors
let
p = the number of pennies the boy puts into the money box each week, p>1, p is integer
£1.04 = 104 p
after a few weeks (lets say n weeks) there was a total of 65p
pn = 65
an a few weeks (lets say m weeks) later there was a total of £1.04
pn + pm = 104
65 + pm = 104
pm = 39
now we have
pn = 65 => p|65
pm = 39 => p|39
p|65, p|39, p>1
since 39 = 3*13 we have the following possibilities:
if p = 3 then 3 does not divide 65 follows p is not 3.
Of p = 13 and 13|65 follows the solution is p = 13 p.
Every week the boy puts 13 pennies into the money box.