Question

Convert the following word sentence as a mathematical statement involving a polynomial and then solve it:

"The sum of the least and greatest of three consecutive odd integers is 158. What is the middle (second) of the three integers?"

Answer 1

To solve the problem, assign variables to the consecutive odd integers (x, x+2, x+4). Then, write and solve the polynomial equation x + (x+4) = 158 to find the value of x. The middle (second) odd integer is x+2.

Step-by-step explanation:

To convert the word sentence into a mathematical statement, let's assign variables to the three consecutive odd integers. Let the first odd integer be x, the second (middle) odd integer be x+2, and the third odd integer be x+4. According to the given information, the sum of the least (x) and greatest (x+4) of the three consecutive odd integers is 158. So, the polynomial equation representing this information is:

x + (x+4) = 158

To solve this equation, we can combine the like terms on the left side:

2x + 4 = 158

Next, we can isolate the variable x by subtracting 4 from both sides of the equation:

2x = 154

Now, divide both sides of the equation by 2 to solve for x:

x = 77

Therefore, the middle (second) odd integer is x+2, which is equal to 79.