Math CentralQuandaries & Queries

Question from Pleroma:

The product of two alternate odd integers exceeds three times the smaller number by 12.
What is the larger number?


Every odd integer is 1 more than an even number and every even number can be written $2n$ for some integer $n.$ Thus every odd integer can be written $2n + 1$ for some integer $n.$

Suppose that $2n + 1$ is the smaller of your two odd integers than the next odd integer is 2 more than than so it is $2n + 3.$

What is the product of these two odd integers?

What is 3 times the smaller of the two odd numbers? What is 12 more than that.

This gives you a quadratic equation is $n.$ Solve for $n.$

Make sure you verify your answer.


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