Question

The sum of two integers is 20. The product of the same two integers is 96. What is the smaller of the 2 integers?

OPTION 1: 8
OPTION 2: 12
OPTION 3: 4
OPTION 4: 16

Answer 1

The system of equations is solved by finding two integers whose sum is 20 and whose product is 96. Factoring the resulting quadratic equation gives us the integers 4 and 16, with 4 being the smaller of the two. Thus, the answer is OPTION 3: 4.

Step-by-step explanation:

The question given is a system of equations problem where we need to find two integers whose sum is 20 and whose product is 96. To solve this, we need to identify two numbers that satisfy both conditions. Let's denote the two integers as x and y. The first equation is x + y = 20, and the second is xy = 96.

Step by Step Solution:

1. Start with the equations:
   
2. Assume x is the smaller integer, then we can express y as 20 - x.
3. Replace y in the second equation: x(20 - x) = 96.
4. This simplifies to a quadratic equation: -x^2 + 20x - 96 = 0.
5. Factor the quadratic equation to find the integer solutions.
6. The factors of 96 that add up to 20 are 4 and 16, as 4 * 16 = 96 and 4 + 16 = 20.
7. Therefore, the two integers are 4 and 16. Since 4 is the smaller integer, that is our answer.

The smaller integer in this system of equations is 4, which corresponds to OPTION 3: 4.