Mia is three years older than twice her sister brooke's age. the sum of their ages is less than 30. what is the greatest age brook can be ?

Whenever you see the phrases "less" or "greater," it's usually a pretty good indicator that you're going to be dealing with inequalities in some way or another.

As with most word problems, our "setup" should involve first giving a label to our unknowns. We don't know what Brooke's age is, so let's label that with the variable b. We know that Mia is three years older than twice Brooke's age, which, using our new variable, can be modeled with the expression m = 2b + 3, where the variable m represents Mia's age.

We're also given that the sum of their ages is less than 30, or, translated into an inequality:



We already know that m = 2b + 3 though, so we can rewrite everything in terms of Brooke's age, b:



From there, simply solve for b and you'll have your upper limit.