if x, y, and z are positive numbers, with xy = 24, xz = 48, and yz = 72, what is x + y + x? please explain how you got tha answer too. thank you.
xz = 48
yz = 72
xy = 24
x = 4, y = 6, z = 12
x + y + z = 4 + 6 + 12 = 22
I did this manually, by trial an error
there must be an easier way ?
I am not a tutor
maybe a tutor will answer with an easier way
To find the values of x, y, and z, we can solve a system of equations. We have three equations: xy = 24, xz = 48, and yz = 72.
Let's start by finding the value of x. We have xy = 24, so if we divide both sides of the equation by y, we get x = 24/y.
Now, let's substitute this value of x into the equation xz = 48. We have (24/y)z = 48. If we multiply both sides of the equation by y, we get 24z = 48y. Dividing both sides by 24, we get z = 2y.
Finally, let's substitute the values of x and z into the equation yz = 72. We have y(2y) = 72. Simplifying, we get 2y^2 = 72. Dividing both sides by 2, we have y^2 = 36. Taking the square root of both sides, we get y = 6.
Using the value of y, we can find x and z. From x = 24/y, we have x = 24/6 = 4. And from z = 2y, we have z = 2 * 6 = 12.
To find x + y + z, we simply add the values of x, y, and z: 4 + 6 + 12 = 22.
Therefore, x + y + z = 22.