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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, May 2019

2019-07-09

Pocket Money

How much money is in her saving account?

Laura wants to buy a smartphone and agrees to an installment payment plan. She has to pay 20 dollars in the first month, 30 dollars in the second month, 40 dollars in the third month, and a final payment of 90 dollars in the fourth month.

Once at home, Laura notes that she does not have enough money in her savings account to pay each installment. So, her father makes the following offer: before each payment is due, he will double the existing amount in her savings account. Laura is very happy with this offer and realizes that she will have exactly the same amount of money in her savings account at the end of the smartphone payment plan as she did when she started.

How much money does Laura have in her savings account?

Solution

The formulas below represent each installment:
x = amount in the savings account

Installment 1: a = 2x - 20
Installment 2: b = 2a - 30
Installment 3: c = 2b - 40
Final installment: x = 2c - 90

Insert the formula for installment 3 into that of the final installment:
x = 2*(2b – 40) – 90
x = 4b – 170

Then, insert the formula for installment 2:
x = 4*(2a – 30) – 170
x = 8a – 290

Finally, insert the formula for installment 1:
x = 8*(2x – 20) – 290
x = 16x – 450
15x = 450
x = 30

Laura has 30 dollars in her savings account.

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