Write two-variable inequalities: word problems

Convert constraints from context into two-variable inequalities.

Lesson 3

Concept

Identify quantities, define variables, and translate phrases like “at most,” “at least,” and “no more than” into symbols.

Tickets cost $8 for students and $12 for adults. Revenue must be at least $240. Write an inequality.

“At most 50 total” translates to:

x + y ≥ 50

x + y ≤ 50

x - y = 50

x + y > 50

“At least” corresponds to:

≤

≥

These steps are out of order — can you fix them?

1.Define variables

2.Translate each phrase

3.Combine into inequality

4.Interpret and check units

Why should variable definitions include units?