The difference of two numbers is 96 and their sum is 300. Find the numbers. What is the answer for that?
x-y = 96
x+y = 300
solve that, or reason thusly:
150+150=300
difference is zero
The difference is 96, so subtract 48 from one number and add 48 to the other:
102+198 = 300
difference is 96
To find the two numbers, we can set up a system of equations. Let's call the first number x and the second number y.
According to the problem, we have two conditions:
1. The difference of two numbers is 96: x - y = 96.
2. The sum of two numbers is 300: x + y = 300.
We now have a system of equations:
x - y = 96 ...(Equation 1)
x + y = 300 ...(Equation 2)
To solve this system, we can use the method of elimination or substitution. Let's use the method of elimination:
Add Equation 1 and Equation 2:
(x - y) + (x + y) = 96 + 300
This simplifies to:
2x = 396
Divide both sides by 2 to solve for x:
2x/2 = 396/2
x = 198
Now substitute x = 198 into either Equation 1 or Equation 2 to solve for y. Let's use Equation 2:
198 + y = 300
Subtract 198 from both sides:
y = 300 - 198
y = 102
So, the two numbers are x = 198 and y = 102.