Answer:
Smaller of the two numbers = 90
Explanation:
We will need a system of equations to find the two numbers, where:
- A represents one number,
- and B represents the other number.
First equation:
Since one number is twelve less than the other number, our first equation is given by:
A = B - 12
Second equation:
- The average of a set of numbers is the sum of the numbers divided by the amount of numbers in the set.
Since there are two numbers and the average of the numbers is 96, our second equation is given by:
(A + B) / 2 = 96
Method to solve: Substitution:
We can solve for B by substituting A = B - 12 for A in (A + B) / 2 = 96.
(B - 12 + B) / 2 = 96
((2B - 12) / 2 = 96) * 2
(2B - 12 = 192) + 12
(2B = 204) / 2
B = 102
Thus, one of the numbers is 102.
Solving for A:
We can solve for A by plugging in 102 for B in A = B - 12:
A = 102 - 12
A = 90
Thus, the other number is 90.
Out of the two numbers, 90 is the smaller number.