The larger of two number is 15 more than three times the smaller number. if the sum of the two numbers is 63, find tge numbers.

To solve this we will write an equation to describe the situation.
(For some fun let us use (Apple) to represent the smaller number, and (Pineapple) for the big number)

Basically what the question is telling us is:
 (apple) + (pineapple)  = 63

Now we need to know what and (apple) and (pineapple)   are.
(pineapple) = 15 more than 3x the smaller number = 3(apple)   +  15
(apple): nothing special to do to it so it is just (apple)

Now we can replace (pineapple)  with what we calculated above. (pineapple) = 3(apple)  +  15

This means (apple)  + (3(apple)  + 15) = 63

  (apple) + 3(apples)  is simply 4(apples) 

So, the equation is now 4(apples)  + 15 = 63

Now lets solve for (apple)  .
4(apple)  + 15 = 63
4(apple)  = 63 - 15
4(apple) = 48
(apple)= 48 ÷ 4

(apple) = 12
Voila! Now we know what (apple) is, but we still need to find (pineapple)  .

Remember how  (pineapple)  = 3(apple)   +  15 ?
We know (apple)  = 12 so plug in 12 for (apple)  to find out what (pineapple)   is.

  (pineapple) = 3(12) + 15
  (pineapple) = 36 + 15
  (pineapple) = 51

Now just to check: (apple)   +  (pineapple) should equal 63
Does 12 + 51 = 63? YES! so this answer is correct.

The two numbers you are looking for are:
apple = smaller number = 12
pineapple = bigger number = 51

X is the smaller number. 3x + 15 is the larger number. So x + 3x + 15 = 63. 4x + 15 = 63.
4x = 48. x = 12. (Smaller number) The larger 36 + 15 or 51.