Laura wants to buy a smartphone and agreed to an installment payment plan. The seller lured her with low starting rates which rise quickly afterwards. Thus, she has to pay 20 dollars in the first month, 30 dollars in the second month, 40 dollars in the third month, and in the fourth month a final installment payment of 90 dollars.
Once at home, Laura notes that she does not have enough money in her savings account for the installment payments. After she had complained about this shortfall to her father, he made the following offer: Before each installment payment, he will double the existing amount in her savings account. Laura is very happy with this offer and realizes after a short consideration 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?
The formulas below represent the three installments and final installment:
x = amount in the savings account
1. installment: a = 2x - 20
2. installment: b = 2a - 30
3. installment: c = 2b - 40
Final installment: x = 2c - 90
Insert the formula of the 3. installment into the final installment:
x = 2*(2b – 40) – 90
x = 4b – 170
Insert the formula of the 2. installment:
x = 4*(2a – 30) – 170
x = 8a – 290
Insert the formula of the 1. installment:
x = 8*(2x – 20) – 290
x = 16x – 450
15x = 450
x = 30
Thus, Laura has 30 dollars in her savings account.