Pete's parents are offering to pay him a weekly allowance for doing his chores. They've given him two different payment options for a period of 15 weeks.

Option 1: $20 every week

Option 2: A penny in the first week, and then double the amount from the previous week in each week after that. So, 1 penny in the first week, 2 pennies in the second week, 4 pennies in the third week, and so on.

Which one is the better option for Pete? Explain why.

Question

Mathematics

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24 January, 18:03

Pete's parents are offering to pay him a weekly allowance for doing his chores. They've given him two different payment options for a period of 15 weeks.

Option 1: $20 every week

Option 2: A penny in the first week, and then double the amount from the previous week in each week after that. So, 1 penny in the first week, 2 pennies in the second week, 4 pennies in the third week, and so on.

Which one is the better option for Pete? Explain why.

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Answers (1)

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Jaylin Downs · Answer 1

Find the total of each option to see which one is better.

Option 1:

$20 every week for 15 weeks = 15 x 20 = $300 total.

Option 2:

Week 1 you have 1 penny.

Week 2 you would have 1 + 2 = 3 pennies.

Week 3 you would have 3 + 4 = 7 pennies.

From this we can see a pattern of 2^x - 1 where x is the number of weeks.

So in 15 weeks he would have 2^15 - 1 = 32767 pennies.

100 pennies equal $1

32767 / 100 = $327.67

The second option is better because he ends up with more money.