Answer:
The numbers are 30, 60, and 10
Explanation:
Let's start by assigning variables to the three numbers.
We can call them x, y, and z.
From the problem, we know that:x + y + z = 100
We also know that the first number is a multiple of 15, so we can write:
x = 15a, where a is some integer.
Furthermore, we know that the second number (y) is ten times the third number (z), so we can write:
y = 10z
Now we can substitute equations (2) and (3) into equation (1) to get an equation in terms of z:
15a + 10z + z = 100
Simplifying, we get:
15a + 11z = 100
To find a possible solution for this equation, we can try different values of a and see if we get a whole number solution for z.
Let's start with a = 1. Substituting a = 1, we get:
15(1) + 11z = 100
z = (100 - 15)/11
z = 8.64
Since z is not a whole number, we need to try a different value of a.Let's try a = 2.
Substituting a = 2, we get:15(2) + 11z = 100
z = (100 - 30)/11
z = 6
Now we have a whole number solution for z. Substituting z = 6 into equations (2) and (3), we get:x = 15a = 15(2) = 30
y = 10z = 10(6) = 60So the three numbers are 30, 60, and 10.