Two friends, Sophia and Ruby, took summer jobs. The equation y = 23.9x represents Ruby’s earnings in dollars and cents, y, for working z hours. Sophia earned $1098.20 in 38 hours.
The correct answer and explanation is:
To find Ruby’s hourly rate, we can use the equation y=23.9xy = 23.9x, where yy represents earnings in dollars and cents, and xx represents hours worked. This equation means that Ruby earns $23.90 for each hour worked.
Now, let’s focus on Sophia. Sophia earned $1098.20 for 38 hours. To find her hourly rate, we divide her total earnings by the number of hours worked: Hourly rate for Sophia=1098.2038=28.9\text{Hourly rate for Sophia} = \frac{1098.20}{38} = 28.9
So, Sophia’s hourly rate is $28.90.
Now, we can compare the two friends’ hourly rates:
- Ruby earns $23.90 per hour.
- Sophia earns $28.90 per hour.
Sophia earns more per hour than Ruby. This could be due to differences in the type of work they did or the nature of their jobs. Ruby’s hourly rate is lower, but if she worked more hours than Sophia, she might have earned more overall, depending on the total number of hours each worked.
To summarize, Sophia’s hourly rate is $28.90, which is higher than Ruby’s hourly rate of $23.90.