AlgebraVery hardInterpreting the number of solutions of a system in context
Algebra practice question
Two phone plans are compared. Plan A costs 20 + 0.05m dollars for m minutes; Plan B costs 20 + 0.05m dollars as well, after a discount. Which statement about the number of minutes for which the plans cost the same is true?
- A. The plans cost the same for every number of minutes, so there are infinitely many such values of m.Correct
- B. The plans cost the same for exactly one value of m.
- C. The plans never cost the same.
- D. The plans cost the same only when m = 0.
Answer: A. The plans cost the same for every number of minutes, so there are infinitely many such values of m.
The two cost expressions are identical, so the plans agree for all m.
Why the other answers are wrong
- B. The plans cost the same for exactly one value of m.
- Identical expressions don't meet at a single point; they coincide everywhere.
- C. The plans never cost the same.
- They are equal for every m.
- D. The plans cost the same only when m = 0.
- They are equal at m = 0 and at every other m too.
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