AlgebraHardTwo-stage problem: solve a system, then apply a change
Algebra practice question
A café sells coffee at $3 a cup and tea at $2 a cup. On Monday it sold 80 cups in total for $220. On Tuesday it sold twice as many coffees as on Monday and half as many teas. What was the café's revenue, in dollars, on Tuesday?
Answer: 380
Monday: c + t = 80 and 3c + 2t = 220. From the first, t = 80 − c; then 3c + 160 − 2c = 220, so c = 60 and t = 20. Tuesday: 120 coffees and 10 teas, so revenue = 3(120) + 2(10) = 360 + 20 = $380.
Common wrong answers
- If you answered 220
- 220 is Monday's revenue.
- If you answered 400
- 400 comes from 3(120) + 2(20), forgetting to halve the teas.
- If you answered 440
- 440 doubles Monday's revenue, but only the coffees doubled; the teas halved.
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