**Answers for Christmas Present Problems**

December 21, 2017

There are two different approaches to solve the problem.Â One method involves using a method of trial and error;Â the other method involves using algebra.

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1. Trial and Error

Choose a number, for example, 6.Â Try 6 as the number of presents that Davina has.

6 + (2 x 6) + (2 x 6 + 10)

6 +Â Â 12Â Â Â + (12Â Â + 10)Â Â = 40

This leaves 40 which is too much so try a smaller starting number.Â

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This time choose a number smaller than 6, like 4.

4 + (2 x 4 ) + (2 x 4 + 10)

4Â +Â Â Â Â 8Â Â Â +Â (8Â Â Â + 10)

4Â +Â Â Â 8 +Â Â Â Â 18Â Â Â Â Â Â = 30

This works!

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2. â€‹Algebra

Choose a letter of the alphabet to represent the unknown number of presents that Davina has. Â The letter that has been chosen in this case is n.

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Re-organise Â the ns by counting them all up and grouping them together. Â

Then, whatever calculation is performed Â on one side of the equation must be done on the other side as well. Â See the purple calculations.

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Always go back and check the calculations with the answer you have found.Â See the equation below.Â The white text shows n.Â

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Which method did you use?Â Hopefully, you'll be able to solve this type of problem next time.

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