AlgebraVery hardCost of a third combination
Algebra practice question
Three pens and two notepads cost $11. Five pens and four notepads cost $20. How much, in dollars, do two pens and three notepads cost?
Answer: 11.5 or 23/2
Let p and d be the prices. 3p + 2d = 11 and 5p + 4d = 20. Doubling the first gives 6p + 4d = 22; subtracting gives p = 2, then d = 2.5. So 2(2) + 3(2.5) = 11.5.
Common wrong answers
- If you answered 9
- 9 uses d = 1.5, a slip in solving for d.
- If you answered 11
- 11 copies the first total; the combination asked for is different.
- If you answered 10.5
- 10.5 comes from swapping the two prices.
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