Question

Can you find two consecutive odd integers such that twice the smaller one is 13 less than three times the larger one?

Answer 1

The two consecutive odd integers that satisfy the given condition are 7 (the smaller one) and 9 (the larger one), which we found by solving the equation 2n = 3(n + 2) - 13.

Step-by-step explanation:

The task is to find two consecutive odd integers where the condition twice the smaller one is 13 less than three times the larger one holds true.

Let's denote the smaller odd integer as 'n'. Since we're looking for consecutive odd integers, the next odd integer is two units larger, so we will denote the larger one as 'n + 2'.

The given condition can be written as an equation:
2n = 3(n + 2) - 13

Solving the equation:

1. Multiply out the right-hand side: 2n = 3n + 6 - 13
2. Simplify the right-hand side: 2n = 3n - 7
3. Isolate the variable 'n' on one side: n = 7
4. The smaller odd integer (n) is 7, and the next consecutive odd integer (n + 2) is 9.

Therefore, the two consecutive odd integers are 7 and 9.