Questionnomework11.1: Problem / (1 point)
A 30-second commercial during Super Bowl XLII in 2008 cost advertisers 2.7 million. For the first Super Bowl in 1967, an advertiser could have purchased approximately 26.19 minutes of advertising time for the same amount of money. (a) Assuming that advertising cost is proportional to its length of time, find the cost of advertising, in dollars/second, during the 2008 Super Bowl. cost $=$ $\square$ dollars/second. (round to nearest cent and do not enter commas) (b) Assuming that advertising cost is proportional to its length of time, find the cost of advertising, in dollars/second, during the 1967 Super Bowl. cost $=$ $\square$ dollars/second. (round to nearest cent and do not enter commas) (c) How many times more expensive was Super Bowl advertising in 2008 than in 1967? $\square$ times more expensive (round to nearest whole number)

Studdy Solution

STEP 1

1. The cost of advertising is proportional to its length of time.
2. In 2008, a 30-second commercial cost $2.7$ million.
3. In 1967, $2.7$ million could buy approximately $26.19$ minutes of advertising.
4. We need to find the cost in dollars per second for both years and compare them.

STEP 2

1. Calculate the cost per second for the 2008 Super Bowl.
2. Calculate the cost per second for the 1967 Super Bowl.
3. Compare the costs to determine how many times more expensive the 2008 Super Bowl was compared to 1967.

STEP 3

Calculate the cost per second for the 2008 Super Bowl.
Given: - Cost for 30 seconds = $2.7$ million.
Convert the cost to dollars per second:
$\text{Cost per second in 2008} = \frac{2,700,000}{30}$
Calculate:
$\text{Cost per second in 2008} = 90,000$

STEP 4

Calculate the cost per second for the 1967 Super Bowl.
Given: - Cost for $26.19$ minutes = $2.7$ million.
Convert minutes to seconds:
$26.19 \text{ minutes} = 26.19 \times 60 \text{ seconds}$
$26.19 \times 60 = 1571.4 \text{ seconds}$
Convert the cost to dollars per second:
$\text{Cost per second in 1967} = \frac{2,700,000}{1571.4}$
Calculate:
$\text{Cost per second in 1967} \approx 1718.98$

STEP 5

Compare the costs to determine how many times more expensive the 2008 Super Bowl was compared to 1967.
$\text{Times more expensive} = \frac{\text{Cost per second in 2008}}{\text{Cost per second in 1967}}$
$\text{Times more expensive} = \frac{90,000}{1718.98}$
Calculate:
$\text{Times more expensive} \approx 52$
The cost of advertising during the 2008 Super Bowl was approximately $\boxed{52}$ times more expensive than in 1967.

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