What is the awenser to what is the sum to 15 but a diffrece of 3?

The two numbers are 9 and 6

We can deduce from the question that we need 2 numbers. Lets start by defining the two numbers.


Define the two numbers

Let one number be x and the other number be y.


Construct the first equation (Sum)

The sum of the two numbers is 15.
x + y = 15


Construct the second equation (Difference)

The difference of the numbers is 3
x - y = 3


Use the two equations to solve x and y

x + y = 15 (equation 1) 
x - y = 3    (equation 2) 


Make x the subject in equation 2

x - y = 3              ← Add y to both sides
   + y  +y
x = 3 + y     


Substitute x = 3 + y into equation 1

x + y = 15                   ←Substitute x = (3+y)
(3 + y) + y = 15
3 + y + y = 15            ←Combine like terms
2y + 3 = 15                ←take away 3 from both sides
    -3       -3
2y = 12                      ←Divide by 2 on both side to get 1 y
÷2    ÷2
y = 6

Now we know y =6, substitute it into equation 1 to find x


Substitute y = 6 into equation 1 to find x

x + y = 15                     ←Substitute y = 6
x + 6 = 15                     ←take away 6 from both sides
     -6    -6
x = 9

Now we know x = 9


Find the two numbers

first number = x = 9
second number = y = 6


The two numbers are 9 and 6