3.3.11 Calculator Exploration—A Practical Problem

Let’s return to the calculator for a practical problem.

Calculator symbol The calculator can be accessed in the left-hand side bar under Toolkit.

Try each part of the question below. Don’t panic if you can’t see how to get the answer right away. The hints will give you some direction.

Activity symbolActivity: The Great Malvern Priory

The Great Malvern Priory in England is a church dating back more than 900 years. It contains magnificent stained glass, medieval wall tiles, and beautiful carved monks’ seats. In 2011, there was a notice posted at the entry to the priory, reading: “This Priory Church costs £3 every 5 minutes.” Visitors are encouraged to leave a donation of £2.50.

(a) To maintain the priory costs £3 (three British pounds) every five minutes. Use the calculator to find out how much it costs (in British pounds) in one year (365 days).

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Discussion

How many times do you have “five minutes” in one hour? Use this to find the cost per hour. Now, how many hours are in a day, and how many days are in a year?

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Answer

(a) There are 12 stretches of five minutes in each hour, and 24 hours in each day. Therefore, the cost for a year of 365 days will be equation left hand side pound times three multiplication 12 multiplication 24 multiplication 365 equals right hand side pound times 315360. The cost of running the priory for a year is £315,360.

(b) In 2011, one British pound was equivalent to about 1.55 U.S. dollars. How much will it cost an American visitor (in U.S. dollars) when he or she donates £2.50 to the Priory?

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Discussion

To buy one British pound, an American had to pay $1.55. The visitor then donates £2.50.

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Answer

(b) Since equation left hand side 2.5 multiplication dollar times 1.55 equals right hand side dollar times 3.875, it will cost the American visitor about $3.88 (rounded to the nearest cent).

(c) Calculate how much the Priory would cost to run for a year in U.S. dollars, using the same exchange rate as before (£1 costs $1.55).

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Discussion

If you find this calculation difficult, then think of a simpler version first. One British pound is equivalent to 1.55 U.S. dollars, so two British pounds would give twice as many dollars—multiply by 2. So, how many dollars would you get for £315,360?

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Answer

(c) equation sequence pound times 315360 equals dollar times 1.55 multiplication 315360 equals dollar times 488808 So the cost in US dollars is $488,808.

(d) You found that the cost for a year is £315,360. If each visitor to the Priory leaves the suggested donation of £2.50, how many visitors are needed in a year to cover the cost? How many does that make per day?

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Discussion

If you’re not sure how to do this, then think of a similar problem with easier numbers. Suppose that the total cost was £100, and each visitor donated £5. To find the number of visitors necessary, you would need to divide £100 by £5. This makes 20, and you know that this is right, because 20 visitors at £5 each will give £100. Can you apply the same method to this bigger problem? When you have found the number of visitors needed per year, you can divide this by the number of days in a year to find  how many people have to donate each day in order to raise the money needed.

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Answer

Dividing £315,360 by £2.50 gives 126,144. So, 126,144 visitors would be needed each year to cover the total cost by paying £2.50 each. Dividing by 365, this comes out at 345.6, which is nearly 350 paying visitors that will have to contribute each day to cover the cost of maintaining the church.

Well done: you used the calculator to solve a mathematical problem from the real world!

Did you write out the workings that you used to get to your answer in your math notebook? It is good to get into this habit for a few reasons. Firstly, it makes it easier for you to check back over your work, following your own reasoning, and checking for possible errors. Also, if you are going to have your work graded or marked, then your teacher can see everything you have done.  They can then give you credit for what you have done well and be able to help out if they spot any problems. Never just put the answer down without showing how you got to it.

3.3.10 Using a Related Problem

3.3.12 Multiplication and Division Puzzle