Question

The second of three numbers is 8 more than the first,

and the third number is 3 less than 3 times the first.
If the third number is 15 more than the second, find
the three numbers.
1st.
2nd
3rd

Answer 1

Let's start by assigning variables to the three unknown numbers. Let x be the first number, y be the second number, and z be the third number.

According to the problem statement, we have:

y = x + 8 (the second number is 8 more than the first)
z = 3x - 3 (the third number is 3 less than 3 times the first)
z = y + 15 (the third number is 15 more than the second)
We can use the first equation to substitute y in the second and third equations, as follows:

z = 3x - 3 (the third number is 3 less than 3 times the first)
z = (x + 8) + 15 (the third number is 15 more than the second)
3x - 3 = x + 23 (substituting y = x + 8 and z = y + 15)
2x = 26
x = 13
Now that we know x, we can use the first equation to find y:

y = x + 8
y = 13 + 8
y = 21
Finally, we can use any of the equations to find z:

z = y + 15 (the third number is 15 more than the second)
z = 21 + 15
z = 36
Therefore, the three numbers are:

1st: 13
2nd: 21
3rd: 36