Numbers English Contest #16

A car manufacturer is testing out an advertising campaign by using a local TV station. It has identified a particular evening TV show it feels will reach its target audience. The car manufacturer wants to run a half million impressions in the next month to see how this campaign affects sales in this area. If the campaign is successful, it will expand this campaign nationally.

The area serves 240,000 people. The ratings for this TV show are 2.41% of the total population. TV commercials for that show run for $315 for a 30-second spot. How much will it cost to run this test advertising campaign? If the manufacturer's profit is $825 per car sold, how many cars must be sold just to pay for this advertising campaign?   

Solution to Contest #15

First, we take a look at what the questions is asking for.

Which campaign is most effective for Dave, based on a cost per 1000 impressions?

Note that the question did not ask for cost per click.

Next we calculate the cost per 1000 impressions for Campaign #1.

$31.00 / 40,134 x 1000 = $0.772 per thousand impressions.

Next, we do some calculations for Campaign #2. We must think a little to use the information relating to "clicks" appropriately.

Cost = $31.00 x 2.1 = $63.00

Clicks = 158

Click Through Rate = 0.92% = 0.0092

Impressions = 158/0.0092=17,174

Cost per 1000 impressions = $63.00 / 17,174 x 1000 = $3.67 per thousand impressions.

Next, we do some calculations for Campaign #3. 

Cost = $31.00 - $12.25 = $18.75

Clicks = 158 * (1-0.115) = 140

Click Through Rate = 0.92% + 0.54% = 1.46% = 0.0146

Impressions = 140/0.0146 = 9,589

Cost per 1000 impressions = $18.75 / 9,589 x 1000 = $1.96 per thousand impressions. 

Campaign #1 is the most effective campaign, based on cost per thousand impressions. 

Contest #15

Dave is evaluating the effectiveness of his Google ad campaigns for his business English program. Although he is paying on a cost per click basis, he is looking to see which campaign is giving him the most impressions for the least money.

Last month, Campaign #1 cost $31.00. It had 105 clicks and 40,134 impressions.

Campaign #2 cost two point one times as #1. It had 158 clicks and had a click-through rate of zero point nine two percent.

Campaign #3 cost $12.25 less than campaign #1. It had 11.5% fewer clicks than Campaign #1, but had a higher click-through rate than Campaign #2 by zero point five four percentage points. 

Which campaign is most effective for Dave, based on a cost per 1000 impressions?

Solution to Contest #14

• Current holding in $US = $100 + Є100 x $0.75543/Є=$175.54.
• New exchange rate = 0.75543 x (1— 0.026) = 0.73579.
• Future holdings in $US = $100 + Є100 x 0.73579 = $173.58.
• % Change = (173.58 — 175.54) / 175.54 x 100% = —1.1%.

His holding will have dropped by 1.1% by next week if this rate change occurs.    

Contest #14

Jack has US$100 and E100. Today, one US$ buys 0.75543 Euros. If this rate is expected to drop by 2.6% next week, what will be the percent change in his holdings in terms of US$?

Solution to Contest #13

This numbers English contest has lots of numbers English to translate into calculation. It also requires some logic to set up the calculation.

The question seems quite tricky:

What is the expected loss in profit from March to April?

Some of you may be asking: "How can we have a loss in profits?" After all, losses and profits are opposites of each other; we should only have one or the other, right?

To explain this, let's consider a company that has a profit of $2,000 in Month 1 and a profit of $1,500 in Month 2. There is a $500 loss in profits from Month 1 to Month 2. Now do you understand how words are used in this way?

We need to start with the end of March production figures to build our figures for March and April.

At the end of March, an oil well was producing 50.5 m3 of oil per day and 72.1 m3 of water per day. Each month, the well's oil production decreases by 1.855% and water production increases by 2.011%.

To get the figures for the end of April, we simply make these calculations:

Oil rate = 50.5 m3 x (1 - 0.01855) = 49.56 m3 per day.

Water rate = 72.1 m3 x (1 + 0.02011) = 73.55 m3 per day.

Average oil rate = (50.5 + 49.56) /2 = 50.03 m3 per day

Average water rate = (72.1 + 73.55) / 2 = 72.82 m3 per day

Total oil production = 50.03 m3 / day x 30 days = 1,500.9 m3
Total water production = 72.82 m3 / day x 30 days = 2,184.6 m3

The figures for March are going to be more difficult to calculate because the 50.5 and 72.1 are at the end of the month. In English, it is important to base the % calculation on the starting figures, which, in this case, are for the beginning of March, which is what we are trying to solve. So the calculations work like this:

Oil rate = 50.5 / (1 - 0.01855) = 51.45 m3 per day.
Water Rate = 72.1 / (1 + 0.0211) = 70.61 m3 per day.

Average oil rate = (51.45 + 50.5) / 2 = 50.98 m3 per day.
Average water rate = (70.61 + 72.1) / 2 = 71.36 m3 per day.

Monthly oil production = 50.98 x 31 days = 1580.4 m3.
Monthly water production = 71.36 x 31 days = 2,212.2 m3.

The next step is calculating the profits for March and April:

It costs $140,250 to operate this well each month.
[It also costs] $51.90 to process one cubic meter of oil and $15.50 to dispose one m3 of water.

For March the costs are: 140,250 + 51.90 x 1580.4 + 15.50 x 2212.2 = $256,563.
For April the costs are: 140,250 + 51.90 x 1500.9 + 15.50 x 2184.6 = $252,008.

Oil price is expected to be $575.00 per m3.

Supposedly, the petroleum company already knew the price of oil in March, but this figure was not provided. The "expected" price is for April. Because this information is somewhat vague, we can only use the best information we have. We will assume that the oil price for both months is $575.00 per m3.

March revenues = 1580.4 x 575.00 = $908,730
April revenues = 1500.9 x 575.00 = $863,018.

What is the expected loss in profit from March to April?

March profit = $908,730 - $256,563 = $652,157
April profit = $863,018 - $252,008 = $611,010

So the loss in profits (from March to April) is $652,157 - $611,010 = $41.147

If you were watching your calculations closely, much of this loss in profits can be attributed to March having one extra day.

Contest #13

At the end of March, an oil well was producing 50.5 m3 of oil per day and 72.1 m3 of water per day. Each month, the well's oil production decreases by 1.855% and water production increases by 2.011%. It costs $140,250 to operate this well each month, which including operator salary and amortization of equipment. Additional costs are $51.90 to process one cubic meter of oil and $15.50 to dispose one m3 of water. Oil price is expected to be $575.00 per m3. What is the expected loss in profit from March to April?