Final answer:
Ms. Bell's hourly rate for piano lessons is $40 when simplified from the given rate of $30 for 3/4 of an hour.
Step-by-step explanation:
The question asks to find Ms. Bell's hourly rate given that piano lessons cost $30 for 3/4 of an hour. To find the hourly rate, we need to calculate how much would be paid for a full hour.
We do this by setting up a proportion where $30 is to 3/4 of an hour as the unknown hourly rate (let's call it x) is to 1 hour. The proportion looks like this: $30 / (3/4) = x / 1. Solving for x gives us x = $30 / (3/4). Multiplying both sides by the reciprocal of 3/4, we get x = $30 * (4/3). So, the hourly rate is x = $40.