Let's determine which student's claimed equation correctly represents the relationship between the number of tickets sold and the amount donated by the local business.
1. Understand the Given Donation Rate: The business donates \[tex]$5.00 for every 10 tickets sold.
2. Identify the Donation per Ticket:
- To find out how much is donated per ticket, we divide the total donation (\$[/tex]5.00) by the number of tickets (10). This calculation gives us the donation amount per single ticket sold.
- [tex]\[
\text{Donation per ticket} = \frac{\$5.00}{10 \text{ tickets}} = \$0.50 \text{ per ticket}
\][/tex]
3. Formulate the Equation:
- Let [tex]\( x \)[/tex] represent the number of tickets sold.
- Let [tex]\( y \)[/tex] represent the total dollars donated.
- Since each ticket contributes \[tex]$0.50 to the donation, the total donation \( y \) is calculated by multiplying the number of tickets \( x \) by \$[/tex]0.50.
- Therefore, the equation that expresses this relationship is:
[tex]\[
y = 0.5x
\][/tex]
4. Assess Student Claims:
- Student A's Claim: [tex]\( y = 2x \)[/tex]:
- This equation suggests that for every ticket sold, \[tex]$2.00 is donated. Considering the actual donation is \$[/tex]0.50 per ticket, this claim is incorrect.
- Student B's Claim: [tex]\( y = \frac{1}{2}x \)[/tex]:
- This equation is equivalent to [tex]\( y = 0.5x \)[/tex], which matches our calculated rate of \$0.50 per ticket. Therefore, this claim is correct.
5. Conclusion:
- Based on the correct calculation and matching equation with the given donation rate, Student B is correct.
