A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $30 and then an additional cents per minute of use. In Plan B, the customer pays a monthly fee of $34.60 and then an additional 6 cents per minute of use.
For what amounts of monthly phone use will Plan A cost no more than Plan B?
Use m for the number of minutes of phone use, and solve your inequality for m
For Plan A, the cost is $30 + cents per minute, and for Plan B, the cost is $34.60 + 6 cents per minute.
So we have the inequality 30 + cents/m ≤ 34.60 + 6 cents/m.
To solve this inequality, we can subtract 30 and 6 cents/m from both sides to isolate the variable:
cents/m ≤ 34.60 - 30 + 6 cents/m.
Next, we can combine like terms:
cents/m ≤ 4.60 + 6 cents/m.
To eliminate the fraction, we can multiply every term in the inequality by m:
cents ≤ 4.60m + 6 cents.
Finally, we can subtract 6 cents from both sides to isolate the variable:
cents - 6 cents ≤ 4.60m.
Simplifying gives:
-5 cents ≤ 4.60m.
To solve for m, we can divide both sides by 4.60:
-5 cents / 4.60 ≤ m.
This gives us the final answer:
m ≥ -1.087 cents.
Therefore, for any amount of monthly phone use (m) greater than or equal to -1.087 cents, Plan A will cost no more than Plan B.