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! ;)
