ACT Preparation / Unit 9 ACT 0830 worked example, 60 to 90 seconds
A Two-Unknown Word Problem
The idea
A word problem with two unknowns needs two equations, built in four steps. First, name both unknowns. Second, write one equation for the count of items and one for their total value, or whatever two facts the story gives. Third, solve the system by substitution or elimination. Fourth, answer the question asked, and check both facts.
In practice
Worked example: a theater sold 300 tickets, adults at $12 and students at $8, for $3,040. Step one: a adult tickets and s student tickets. Step two: a + s = 300 and 12a + 8s = 3,040. Step three: multiply the first by −8, giving −8a − 8s = −2,400, and add: 4a = 640, so a = 160 and s = 140. Step four: 160 + 140 = 300, and 1,920 + 1,120 = 3,040.
Where people slip
The two equations must describe different facts. The count equation written twice in different forms gives a dependent system with no single answer.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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