Problem-Solving and Data AnalysisMediumSolving a model for the input
Problem-Solving and Data Analysis practice question
A model predicts a shop's monthly profit, y, in dollars, from its monthly advertising spend, x, in dollars: y = 4x + 200. According to the model, how many dollars of advertising are needed for a predicted profit of $1,000?
Answer: 200
Set y = 1,000: 4x + 200 = 1,000. Subtract 200: 4x = 800. Divide by 4: x = 200.
Common wrong answers
- If you answered 250
- 250 is 1,000 / 4, ignoring the 200 that the model adds. Subtract the 200 first: 4x = 800.
- If you answered 300
- 300 is (1,000 + 200) / 4 — the 200 was added instead of subtracted.
- If you answered 4200
- 4,200 is 4(1,000) + 200, plugging the profit in as x. The profit is y; the question asks for x.
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