The difference between two numbers is 36. The sum of these two numbers is 62. Find the numbers.
x - y = 36
x + y = 62
x = 36 + y
36 + y + y = 62
2y = 62 - 36
2y = 26
y = 13
Can you take it from there?
Thank you, Sue! That's awesome!
You're welcome, Monica. :-)
To find the numbers, let's represent the two unknown numbers as variables. Let's call the first number "x" and the second number "y".
According to the problem, the difference between the two numbers is 36. This can be expressed as an equation: x - y = 36.
The sum of the two numbers is given as 62. This can be expressed as another equation: x + y = 62.
Now, we have a system of two equations:
Equation 1: x - y = 36
Equation 2: x + y = 62
To solve this system of equations, we can use the method of elimination. We can add the two equations together to eliminate the variable "y":
(x - y) + (x + y) = 36 + 62
This simplifies to:
2x = 98
To isolate the variable "x", we divide both sides of the equation by 2:
2x/2 = 98/2
x = 49
Now that we know the value of "x" is 49, we can substitute it into either of the original equations to solve for "y". Let's use Equation 2: x + y = 62.
49 + y = 62
Subtract 49 from both sides:
y = 62 - 49
y = 13
Therefore, the two numbers are 49 and 13.