The sum of three numbers is

89

. The third number is
3

times the second. The first number is
9

more than the second. What are the numbers?

second --- x

first ---- x+9
third ---- 3x

x + x+9 + 3x = 89

carry on

Always check your answers before you post them.

from my equation:
x + x+9 + 3x = 89
5x = 80
x = 16

according to my definitions:
first = 25
second = 16
third = 48

Is their sum equal to 89 ? , YES
Do they fit the given conditions ?, YES

Yours do not fit the original conditions
Your first is NOT 9 greater than your second.

First number is 9, second number is 20, third number is 60

To solve this problem, we can represent the three numbers as variables. Let's call the first number "x", the second number "y", and the third number "z".

According to the given information:

1) The sum of the three numbers is 89, so we can write the equation:
x + y + z = 89

2) The third number is 3 times the second, so we can write the equation:
z = 3y

3) The first number is 9 more than the second, so we can write the equation:
x = y + 9

Now we have a system of three equations with three variables. We can solve them simultaneously to find the values of x, y, and z.

Substituting equation 3) into equation 1) gives:
(y + 9) + y + z = 89

Substituting equation 2) into equation 1) gives:
(y + 9) + y + 3y = 89

Combining like terms:
5y + 9 = 89

Subtracting 9 from both sides of the equation gives:
5y = 80

Dividing both sides by 5:
y = 16

Now that we know the value of y, we can substitute it back into equations 2) and 3) to find x and z.

From equation 2):
z = 3y
z = 3(16)
z = 48

From equation 3):
x = y + 9
x = 16 + 9
x = 25

So the three numbers are x = 25, y = 16, and z = 48.