AlgebraEasy–MediumUse elimination to find one unknown quantity
Algebra practice question
A science fair organizer buys display tables and poster boards at fixed prices. Two display tables and three poster boards cost a total of $31. Two display tables and one poster board cost a total of $17.
What is the cost, in dollars, of one poster board?
- A. 5
- B. 7Correct
- C. 12
- D. 14
Answer: B. 7
Let x be the cost of a table and y the cost of a poster board. Then 2x + 3y = 31 and 2x + y = 17. Subtracting the second equation from the first eliminates x: 2y = 14, so y = 7 (and then 2x = 17 - 7 = 10, x = 5). Choice A is the cost of one table, the other variable. Choice C comes from adding the equations instead of subtracting: 4x + 4y = 48 gives x + y = 12, the cost of one of each. Choice D is the value of 2y, the result of subtracting without dividing by 2.
Why the other answers are wrong
- A. 5
- That's the cost of one table, not one poster board. After finding y = 7, the question asks for the poster board price.
- C. 12
- You added the two equations instead of subtracting, getting 4x + 4y = 48, or x + y = 12 — that's the cost of one table plus one board.
- D. 14
- Subtracting the equations gives 2y = 14, so you stopped at 2y; divide by 2 to get y = 7.
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