Answer:
Explanation:
Let's begin by assigning variables to represent the three mixed numbers. Let a be the greatest mixed number, b be the middle mixed number, and c be the least mixed number. Then we can write:
a + b + c = 18 (the sum of the three mixed numbers is 18)
a - c = 5 1/5 (the difference between the greatest and least mixed numbers is 5 1/5)
To solve for a, b, and c, we can use substitution. From the second equation, we can solve for a in terms of c:
a = c + 5 1/5
Substituting this expression for a into the first equation, we get:
(c + 5 1/5) + b + c = 18
Simplifying, we get:
2c + b = 12 4/5
Now we need to find three mixed numbers that satisfy this equation. We can start by choosing a value for c. Let's choose c = 2 1/2, which is the smallest possible value for c that will allow the mixed numbers to be non-negative. Then we can solve for b:
2c + b = 12 4/5
2(2 1/2) + b = 12 4/5
5 + b = 12 4/5
b = 7 4/5
Finally, we can solve for a using the equation a = c + 5 1/5:
a = c + 5 1/5
a = 2 1/2 + 5 1/5
a = 7 3/5
Therefore, three mixed numbers that satisfy the conditions of the problem are:
The greatest mixed number: 7 3/5
The middle mixed number: 7 4/5
The least mixed number: 2 1/2
And indeed, their sum is 18 and the difference between the greatest and least mixed numbers is 5 1/5.