To determine the correct function for calculating the student's earnings, we need to consider his earnings from three sources:
1. Earnings per day: The student earns [tex]$15 for each day he works. If he works for \( d \) days, his total earnings from the days will be \( 15d \).
2. Earnings from raffle tickets: The student earns $[/tex]0.25 for each raffle ticket he sells. If he sells [tex]\( r \)[/tex] raffle tickets, his total earnings from the tickets will be [tex]\( 0.25r \)[/tex].
3. Earnings per hour: The student earns $2 for each hour he works. If he works [tex]\( h \)[/tex] hours, his total earnings from the hours worked will be [tex]\( 2h \)[/tex].
The total earnings [tex]\( T \)[/tex] from these three sources can be calculated by summing them up:
[tex]\[ T = 15d + 0.25r + 2h \][/tex]
Now, let's evaluate each of the given options to see which one matches our derived function:
A. [tex]\( T = \frac{15}{d} + \frac{4}{r} + \frac{2}{h} \)[/tex]
This option is incorrect because it involves division, which does not align with the structure of our derived function.
B. [tex]\( T = 15d + 25r + 2 / 2 \)[/tex]
This option is incorrect for two reasons:
- The term [tex]\( 25r \)[/tex] should be [tex]\( 0.25r \)[/tex].
- The term [tex]\( 2 / 2 \)[/tex] results in 1, which does not correspond to any earnings calculation.
C. [tex]\( T = 15d + \frac{r}{4} + 2h \)[/tex]
This option is incorrect because the term [tex]\( \frac{r}{4} \)[/tex] should be [tex]\( 0.25r \)[/tex].
D. [tex]\( T = \frac{d}{15} + \frac{r}{4} + 2 / 2 \)[/tex]
This option is incorrect because it involves division similar to option A and the incorrect term [tex]\( 2 / 2 \)[/tex].
After evaluating all the choices, it is clear that none of the provided options matches our derived function [tex]\( T = 15d + 0.25r + 2h \)[/tex].
Therefore, none of the provided choices are correct. The correct function should be:
[tex]\[ T = 15d + 0.25r + 2h \][/tex]
