This question can be solved by a system of equations.
Let's use x and y to represent the numbers.
"Sum" refers to addition, while "difference" refers to subtraction.
If the sum of x and y is 12, then that means x + y = 12.
If the difference between x and y is 4, then that means x - y = 4, or y - x = 4. Both work since neither are known and their order doesn't change the outcome in the first equation either due to it being addition.
Now we have the system of equations of x + y = 12 and x - y = 4.
{ x + y = 12
{ x - y = 4
To solve this, change one of the equations into slope-intercept form and use the substitution method.
Steps to the substitution method:
- Isolate one of the variables in one of the equations in the system.
- Substitute the expression equal to that variable into the other equation.
- Solve the other equation for a variable.
- If needed, plug the value of the found variable into the still-unknown equation and solve.
Let's isolate x in x - y = 4.
To isolate a variable, remove all other terms from the side of the equation the variable is on by doing the inverse of what is being done to those terms. Remember to do the same thing to both sides!
To isolate x in x - y = 4, add y to both sides.
x - y + y = x
4 + y = 4 + y
x = 4 + y
Now x is isolated!
Now plug the expression equal to x into the other original equation.
x = 4 + y
x + y = 12
(4 + y) + y = 12
We can remove the parentheses without affecting the outcome, since the order of addition doesn't change the result.
4 + y + y = 12
Combine like terms.
The like terms in this case are y and y, which combine to get 2y.
4 + 2y = 12
Isolate the variable.
First, subtract 4 from both sides.
4 + 2y - 4 = 2y
12 - 4 = 8
2y = 8
Divide both sides by 2.
2y / 2 = y
8 / 2 = 4
y = 4
Now we know one of the numbers!
Now we plug the value of this known variable, y, into the other equation in the system so we can find the value of x.
x + y = 12
y = 4
x + 4 = 12
All we have to do is isolate the variable of x by subtracting 4 from both sides!
x + 4 - 4 = x
12 - 4 = 8
x = 8
Now we know both of the numbers!
The numbers who's sum is 12 and difference is 4 is 8 and 4.
Let's check this!
Sum = Addition
Sum of two numbers = 12
8 + 4 = 12
This works! Now let's check the difference!
Difference = Subtraction
Difference of two numbers = 4
8 - 4 = 4
This is true as well, meaning 8 and 4 are the correct answers!
Answers:
8 and 4
Hope this helps!
