Algebra practice question

Answer: 401

Let m be the number of minutes. Plan A costs 54 + 0.09m and Plan B costs 22 + 0.17m. Requiring 54 + 0.09m < 22 + 0.17m gives 32 < 0.08m, so m > 400. Since the inequality is strict, m = 400 makes the two plans cost exactly the same ($90 each), so the least whole number satisfying the condition is 401. Common wrong responses: 400 comes from solving the equation 54 + 0.09m = 22 + 0.17m (or from using ≤ instead of <) and failing to notice that equality is not 'less than'; 123 comes from combining the fees and rates as 32/0.26; 4 comes from dividing 32 by 8 after mishandling the decimal (0.08 treated as 8).

Common wrong answers

If you answered 4

You divided 32 by 8 instead of 0.08 — the decimal matters, and 32/0.08 = 400, so the least whole number is 401.

If you answered 123

You combined the two fees and the two rates as 32/0.26, adding the rates instead of subtracting them; the correct setup is 32 < 0.17m − 0.09m = 0.08m.

If you answered 400

At 400 minutes both plans cost exactly $90, which isn't 'less than' — since the inequality is strict, you need the next whole minute, 401.

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