One ticket to a show costs $\$20$ at full price. Susan buys $4$ tickets using a coupon that gives her a $25\%$ discount. Pam buys $5$ tickets using a coupon that gives her a $30\%$ discount. How many more dollars does Pam pay than Susan?
To compare how much Susan and Pam pay, I need to find the total cost of their tickets after applying their respective discounts. Susan's discount is $25\%$, which means she pays $75\%$ of the full price for each ticket. To find $75\%$ of $20$, I can multiply by $0.75$, which is the decimal equivalent of $75\%$. This gives me $0.75 \times 20 = 15$, so Susan pays $\$15$ per ticket. Susan bought $4$ tickets, so her total cost is $4$ times the cost of one ticket. That is, $4 \times 15 = 60$, so Susan pays $\$60$ in total. Pam's discount is $30\%$, which means she pays $70\%$ of the full price for each ticket. To find $70\%$ of $20$, I can multiply by $0.7$, which is the decimal equivalent of $70\%$. This gives me $0.7 \times 20 = 14$, so Pam pays $\$14$ per ticket. Pam bought $5$ tickets, so her total cost is $5$ times the cost of one ticket. That is, $5 \times 14 = 70$, so Pam pays $\$70$ in total. To find how many more dollars Pam pays than Susan, I can subtract Susan's total cost from Pam's total cost. That is, $70 - 60 = 10$, so Pam pays $\$10$ more than Susan. 