The sum of two numbers is 22. Three times one number increased by five is 35. What are the two numbers?
Let's call the two numbers x and y. We know that:
x + y = 22 (the sum of two numbers is 22)
3x + 5 = 35 (three times one number increased by five is 35)
We can use the first equation to solve for one of the variables. For example, we can solve for y by subtracting x from both sides:
y = 22 - x
Now we can substitute this expression for y into the second equation:
3x + 5 = 35
3x = 30 (subtract 5 from both sides)
x = 10 (divide both sides by 3)
So one of the numbers is 10. We can use the first equation to solve for the other number:
x + y = 22
10 + y = 22 (substitute x = 10)
y = 12
So the two numbers are 10 and 12.