Back to Solve real-world and mathematical problems leading to two linear equations in two variables — Problem 1 · Task Set 40

8.EE.C.8.c Tutor Intake -- Real-World Systems of Equations

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Grade 8·8 problems·~9 min·Common Core Math - Grade 8·standard·8-ee-c-8c

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Concepts

A problem says: "A group bought 12 tickets total, paying $81."
Let $a$ = number of adult tickets and $c$ = number of child
tickets. A student writes only the equation $a + c = 12$ and
tries to solve for both variables. Is this enough information?

No — a single equation in two variables has many solutions (like $(1,11)$ , $(2,10)$ , etc.); a second equation (e.g., about total cost) is needed to pin down a unique answer.

Yes — since there are two variables, one equation is always sufficient to find both.

No — but only because 12 is too large a number to work with in one equation.

Yes, as long as you guess values for $a$ and $c$ that add to 12.