Answer:
The two numbers are 40, and 27.
Explanation:
Since there are only two numbers, with two different aspects, you can just make
a system, and solve.
A sum of two numbers adding up to 67 can be modeled by: x + y = 67.
A difference of those same two numbers being 13 can be modeled by: x – y = 13.
You can add the two equations together to eliminate the y value because the -y and y will cancel out:
x + y = 67.
+ x – y = 13.
And you get: 2x = 80.
Now to find x, just divide by 2 on both sides to cancel out the coefficient of 2 in 2x:
2x = 80
÷2 ÷2
x = 40.
So the first number is 40.
Since we know the first number, we can immediately find the other number by substituting it into the first equation.
x = 40 → x + y = 67
(40) + y = 67
-40. -40
Subtract from both sides to cancel the constant terms.
Then you will get that y or the second number is y = 27.
This is true because 40 + 27 = 67, and 40 - 27 = 13.
