Final answer:
To solve this problem, set up a system of equations using x and y as variables. Substitute one equation into the other to solve for the values of x and y. The larger number is 37 and the smaller number is 21.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let x represent the larger number and y represent the smaller number. From the given information, we have two equations:
x + y = 58
x = y + 16
To solve for x and y, we can substitute the value of x from equation 2 into equation 1:
(y + 16) + y = 58
Combining like terms, we get:
2y + 16 = 58
Subtracting 16 from both sides, we have:
2y = 42
Dividing both sides by 2, we find that y = 21.
Substituting this value back into equation 2, we can solve for x:
x = 21 + 16
So x = 37.
Therefore, the larger number is 37 and the smaller number is 21.