AlgebraEasy–MediumTranslate a context into a system of equations
Algebra practice question
A rooftop greenhouse contains 48 seedling trays, each of which is either a tomato tray or a basil tray. Each tomato tray holds 6 seedlings and each basil tray holds 10 seedlings. Altogether the trays hold 360 seedlings. Let t represent the number of tomato trays and b represent the number of basil trays.
Which system of equations represents this situation?
- A. t + b = 48 and 6t + 10b = 360Correct
- B. t + b = 48 and 10t + 6b = 360
- C. t + b = 360 and 6t + 10b = 48
- D. t - b = 48 and 6t + 10b = 360
Answer: A. t + b = 48 and 6t + 10b = 360
The trays total 48, giving t + b = 48. The seedlings total 360: tomato trays contribute 6t seedlings and basil trays contribute 10b seedlings, so 6t + 10b = 360. Choice B attaches each seedling count to the wrong tray type. Choice C swaps the two totals, using 360 as the number of trays and 48 as the number of seedlings. Choice D misreads 'a total of 48 trays' as a difference between the two tray counts.
Why the other answers are wrong
- B. t + b = 48 and 10t + 6b = 360
- You attached the seedling counts to the wrong tray types — tomato trays hold 6 each (6t) and basil trays hold 10 each (10b).
- C. t + b = 360 and 6t + 10b = 48
- You swapped the two totals: 48 is the number of trays and 360 is the number of seedlings, not the reverse.
- D. t - b = 48 and 6t + 10b = 360
- 'A total of 48 trays' means the two counts add to 48, so t + b = 48, not a difference.
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