Question

1. two tickets to an ice skating performance costs $36.

for five tickets it costs $90, and for nine tickets it
costs $162.
model with math use the graph to determine
whether the number of tickets and the cost have a
proportional relationship. if so, what is the constant
of proportionality and what does it mean?

1. higher order thinking the table and

graph show the costs to buy dvds at
two different stores.
a. which store has the better deal on
dvds? explain.
b. how much money will sheila save if
she buys 20 dvds at the store with
the better deal than at the other store?

Explanation:

Step1: Find unit price for Store A

For Store A, when \(x = 2\), \(y=6.30\). The unit price \(k_A=\frac{y}{x}=\frac{6.30}{2}=3.15\)

Step2: Find unit price for Store B

From the graph of Store B, when \(x = 4\), \(y = 12.80\). The unit price \(k_B=\frac{y}{x}=\frac{12.80}{4}=3.2\)

Step3: Compare unit prices

Since \(3.15<3.2\), Store A has a better deal.

Step4: Calculate cost for 20 DVDs at Store A

Cost at Store A: \(y_A=k_A\times20 = 3.15\times20=63\)

Step5: Calculate cost for 20 DVDs at Store B

Cost at Store B: \(y_B=k_B\times20=3.2\times20 = 64\)

Step6: Calculate savings

Savings \(=y_B - y_A=64 - 63=1\)

Answer:

a. Store A has the better deal. The unit price of DVDs at Store A is \(\$3.15\) (calculated as \(\frac{6.30}{2}\)) and at Store B is \(\$3.2\) (calculated as \(\frac{12.80}{4}\)), and \(3.15<3.2\).
b. Sheila will save \(\$1\).