Question

challenge the ticket price for a concert at a historic music hall includes $6.20 for the concert, $2.10 for the program, and a half restoration fee. the price for 19 tickets is $160.20. how much is the restoration fee?
the restoration fee is $□

Explanation:

Step1: Find single ticket price

$\frac{160.20}{19} = 8.4315789...$

Step2: Sum known per-ticket costs

$6.20 + 2.10 = 8.30$

Step3: Calculate restoration fee

$8.4315789... - 8.30 = 0.1315789...$

Step4: Verify total for 19 tickets

Let $x$ = restoration fee. Total per ticket: $6.20 + 2.10 + x = 8.30 + x$.
Total for 19 tickets: $19(8.30 + x) = 160.20$
$157.70 + 19x = 160.20$
$19x = 160.20 - 157.70 = 2.50$
$x = \frac{2.50}{19} = 0.1315789... \approx 0.13$

Answer:

The restoration fee is $\$0.13$ (or $\$0.13$ per ticket, totaling $\$2.50$ for 19 tickets)