The sum of two numbers is 24. The difference of their squares is 144. What are the two numbers
Let's call one of the numbers x and the other number y.
We know that the sum of the two numbers is 24, so we can set up the equation:
x + y = 24
We also know that the difference of their squares is 144, so we can set up the equation:
x^2 - y^2 = 144
We can rewrite the second equation as:
(x + y)(x - y) = 144
Since we already know that x + y = 24, we can plug that into the equation:
(24)(x - y) = 144
Divide both sides of the equation by 24 to solve for (x - y):
x - y = 6
Now we have two equations:
x + y = 24
x - y = 6
We can solve this system of equations by adding the two equations together:
(x + y) + (x - y) = 24 + 6
2x = 30
Divide both sides of the equation by 2 to solve for x:
x = 15
Now we can substitute the value of x into one of the original equations to solve for y:
15 + y = 24
Subtract 15 from both sides of the equation to solve for y:
y = 9
So the two numbers are x = 15 and y = 9.