Multiple choice

Maria deposits x dollars in a savings account with an annual interest rate of 10%, compounded annually. One year later, she deposits an additional x dollars. If the balance after two years is w dollars, then which expression shows x in terms of w?

  1. w 1 + 1.10

  2. w 1.10 + 1.15

  3. w 1.10 + 1.331

  4. w 1.10 + ( 1.10 ) 2

  5. w ( 1.10 ) 2 + ( 1.10 ) 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The first deposit earns interest for two years and becomes 1.10^2 x, while the second deposit earns interest for one year and becomes 1.10x. Hence w = x[1.10 + (1.10)^2], so x = w/[1.10 + (1.10)^2].

AI explanation

After two years, the initial deposit of x dollars grows to x times 1.10 squared, and the second deposit of x dollars grows to x times 1.10. The total balance w is the sum of these, giving the equation w equals x times 1.21 plus x times 1.10. Factoring out x yields w equals x times 2.31, which means x equals w divided by 2.31. This matches the algebraic expression w divided by the sum of 1.10 and 1.10 squared.

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