Thread: Diophantine eqution problem

Hi I need help to find the answer for the following question this is need to be solving by using the Diophantine equation

Find the number of men, woman and children in a company of 20 persons if together they pay 20 coins, each man paying 3, each woman 2, and each child 1/2.

Originally Posted by dhammikai

Hi I need help to find the answer for the following question this is need to be solving by using the Diophantine equation

Find the number of men, woman and children in a company of 20 persons if together they pay 20 coins, each man paying 3, each woman 2, and each child 1/2.

m - men
w- women
c - children

so we have,
m+w+c=20
3m+2w+(1/2)c=2

Can you proceed now?

Hello, dhammikai!

Find the number of men, woman and children in a company of 20 persons
if together they pay 20 coins, each man paying 3, each woman 2, and each child .

Let: = number of men, = number of women, = number of children.

There are 20 people: . .[1]

They paid a total of 20 coins: . .[2]

Subtract [1] from [2]: .

Since is an integer, must be a multiple of 5.


There are two solutions: .

Thank you very much for your help thanks again