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: The numbers in order are 13, 21, 36

Step-by-step explanation:

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

Sorry it's very long, but it's how I solved this

Hope this helped! ;)

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