AlgebraMediumExtending a linear pattern from a table
Algebra practice question
The total cost of a subscription is a linear function of the number of months. After 1 month the total cost is $14, and after 3 months it is $26. What is the total cost, in dollars, after 6 months?
Answer: 44
The cost rises 26 − 14 = 12 dollars over 3 − 1 = 2 months, so the rate is 6 dollars per month. From month 1 to month 6 is 5 more months: 14 + 5(6) = 44. (Or from month 3: 26 + 3(6) = 44.)
Common wrong answers
- If you answered 38
- 38 is 14 + 4(6) — counting 4 months from month 1 to month 6, but the gap is 5 months.
- If you answered 50
- 50 is 14 + 6(6), adding six months' worth to the month-1 cost, but month 1 is already one of the six months.
- If you answered 84
- 84 is 14 × 6, as if the month-1 cost simply multiplies. It doesn't: the cost has a starting value (8 dollars at month 0) plus 6 per month.
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