Question

Find three consecutive positive odd integers such that the product of the first and the third is five more than eight times the second.

A. 5, 7, 9
B. 9, 11, 13
C. 11, 13, 15
D. 15, 17, 19

Answer 1

To solve the problem, assume the three consecutive positive odd integers are x, x+2, and x+4. Write an equation from the given information and simplify it. Solve the equation to find the values of the integers.

Step-by-step explanation:

To solve this problem, let's assume that the three consecutive positive odd integers are x, x+2, and x+4. According to the given information, the product of the first and the third (x and x+4) is five more than eight times the second (8(x+2)+5).

So we can write the equation as: x(x+4) = 8(x+2) + 5

Simplifying this equation, we get: x^2 + 4x = 8x + 16 + 5

Combining like terms, we have: x^2 - 4x - 24 = 0

Factoring this quadratic equation, we find: (x-6)(x+4) = 0

So the two possible values for x are 6 and -4. However, since we are looking for positive integers, we can discard the negative solution. Therefore, the three consecutive positive odd integers are 6, 8, and 10.