The sum of two numbers is 63. One number is 7 more than the other. Find the numbers.
let one number be x
let the other be x+7
x + x+7 = 63
solve for x, and all that is unknown shall be revealed.
To find the two numbers, let's assign variables to represent them. Let's call one number "x" and the other number "y".
We know that the sum of the two numbers is 63, so we can set up an equation:
x + y = 63
We also know that one number is 7 more than the other, so we can set up another equation:
x = y + 7
Now we have a system of two equations, and we can use algebraic methods to solve for x and y.
One way to solve this system is to substitute the value of y from the second equation into the first equation. By replacing y with (x - 7), we can solve for x:
x + (x - 7) = 63
Combining like terms, we get:
2x - 7 = 63
Next, we can isolate the variable:
2x = 63 + 7
2x = 70
Finally, we solve for x by dividing both sides of the equation by 2:
x = 70 / 2
x = 35
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. If we use the second equation:
y = x - 7
y = 35 - 7
y = 28
So the two numbers are 35 and 28.