Question

Given two consecutive positive odd integers, the product of the larger and twice the smaller is equal to 70. Find the integers.

a) 5 and 7
b) 3 and 5
c) 7 and 9
d) 9 and 11

Answer 1

To find the two consecutive positive odd integers where the product of the larger and twice the smaller equals 70, we solve the quadratic equation (n + 7)(n - 5) = 0 which gives us 5 and 7 as the answer.

Step-by-step explanation:

The question is asking us to find two consecutive positive odd integers where the product of the larger integer and twice the smaller integer equals 70. Let's denote the smaller integer as 'n' and the larger as 'n + 2' because consecutive odd integers differ by 2.

We can set up an equation based on the problem statement:

(n + 2)(2n) = 70

Expanding the left side of the equation gives us:

2n^2 + 4n = 70

Now, subtract 70 from both sides to set the equation to zero:

2n^2 + 4n - 70 = 0

Dividing the entire equation by 2 simplifies it to:

n^2 + 2n - 35 = 0

Factoring the quadratic equation gives us:

(n + 7)(n - 5) = 0

This means n can be either -7 or 5, but since we're looking for positive integers, we choose n = 5. Thus, the consecutive odd integers are 5 and 5 + 2, which is 7. The correct answer is a) 5 and 7.