Question

Eve steps into a supermarket to buy a biro. A biro costs 29 Kobe. She has #2note, and the shopkeeper has 5-kobo and 6-kobo coins in his drawer. If eve is to get her change in these denomination, What is the largest product she can obtain after multiplying the 5-kobo coins by 6-kobo coin in Her change

Answer 1

I know the Kobo is a currency unit of Liberia, but what is a Kobe? What is a #2note ?
Are there 100 Kobo in 1 Naira?

Answer 2

yes
it was a typo I meant Kobo not kobe
100kobo=1naira

2# is 2naira

Answer 3

How do you multiply "5-kobo coins by 6-kobo coin"?

Answer 4

Ok then:
so I will skip writing the units ...
cost = 29
pay with 200
so the change will be 171
number of 5 kobo coins ---- x
number of 6 kobo coins ---- y
5x + 6y = 171
we need whole number solutions for this equation, (called a diophantine equation)

I actually have a method to solve this type using repeating fractions,
but that would be hard to explain here, so ...

by trial and error:
x ---- y
3 26
9 21
15 16
21 11
...
notice since the slope of my line is -6/5, increasing the x by 6 and
decreasing the y by 5 gives me new points.

So we want the largest product of x and y which would be when they
are closest to each other , or

15 and 16 ---> xy = 240

check
5(15) + 6(16) = 171, the amount needed for your change