Question

1. if the original quantity is 15 and the new quantity is 19, which is the best estimate for the percent change?

a 25% decrease
b 5% decrease
c 5% increase
d 25% increase

1. emily and a friend bought two tickets to see a soccer game. each ticket cost $8.25. the friends paid a total of $24.50, which included a fee per ticket for parking near the stadium.

a. how much did each friend pay for the parking fee?

b. what percent increase represents the change when parking is included in the final cost? explain.

Explanation:

Step1: Calculate the total cost of tickets

The cost of one ticket is \( \$8.25\). For two tickets, the cost is \(2\times8.25=\$16.5\)

Step2: Calculate the total parking fee

The total amount paid is \( \$24.50\). The total parking fee is \(24.50 - 16.5=\$8\)

Step3: Calculate the parking fee per person

Since there are two friends, the parking fee per person is \(8\div2 = \$4\)

Step4: Calculate the percent increase for part b

The original cost (for tickets only) is \(C_{original}=16.5\). The new cost (tickets + parking) is \(C_{new}=24.50\). The amount of increase is \(A = 24.50-16.5 = 8\). The percent increase formula is \(P=\frac{A}{C_{original}}\times100\). Substitute \(A = 8\) and \(C_{original}=16.5\) into the formula: \(P=\frac{8}{16.5}\times 100\approx48.5\%\)

Answer:

a. Each friend paid \( \$4\) for the parking fee.
b. The percent increase is approximately \(48.5\%\). The original cost (for tickets) is \( \$16.5\) and the new cost (tickets + parking) is \( \$24.50\). Using the percent - increase formula \(\frac{\text{increase}}{\text{original}}\times100\), with increase \(=24.50 - 16.5=8\) and original \( = 16.5\), we get \(\frac{8}{16.5}\times100\approx48.5\%\)