SOLUTION: 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.

Question 15508: 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.
Answer by smik(40) (Show Source): You can put this solution on YOUR website!
Great Question!

First of all, we must convert all the information given in the question into equations so we can look it from a simplified angle, and hence, solve it.

So, let's start off by giving each of the unknown numbers a name. Let's call the first number a, the second number b, and the third number c.

Therefore:
"The second of three numbers is 8 more than the first" gives us:

b = 8 + a

"... the third is 3 less than 3 times the first" gives us:

c = 3a - 3

and "the third number is 15 more than the second" gives us:

c = 15 + b

Now, we can substitute b = 8 + a into c = 15 + b, to get:

c = 15 + (8 + a), which simplified gives us:

c = 23 + a

With that done we can use elimination.

We've got c = 23 + a, and c = 3a - 3. We want to eliminate 'a', so we should multiply both sides of c = 23 + a by (-3) to get: -3c = -69 - 3a.

Now we can eliminate the 'a' variable:

c = 3a - 3
-3c = -3a - 69
-------------
-2c = -72

Therefore, we can solve for 'c' by dividing both sides by -2, which leaves us with:

c = 36

Now we can plug that value of 'c' into the equation c = 15 + b, to solve for b:

36 = 15 + b (Subtract 15 from both sides)
21 = b

Now that we've got a value for 'b', we can plug it into the equation b = 8 + a to solve for 'a':

21 = 8 + a (Subtract 8 from both sides)
13 = a

And there we have it, the three numbers in order are 13, 21, 36. It's a long process, but it's worth it. Again, Great Question!
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