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Daniela has a three-season acting contract for a new TV show. Her pay for Season 1 is p dollars. Then, her pay will increase by 5 percent from Season 1 to Season 2 and by 10 percent from Season 2 to Season 3. Which of the following represents Daniela's Season 3 pay in terms of p ? Choose 1 answer: (A) 1.15 p (B) (p)/( 1.15) (c) (1.05)(1.1)p (D) (p)/((1.05)(1.1))

Daniela has a three-season acting contract for a new TV show. Her pay for Season 11 is p p dollars. Then, her pay will increase by 55 percent from Season 11 to Season 22 and by 1010 percent from Season 22 to Season 33. Which of the following represents Daniela's Season 33 pay in terms of p p ?\newlineChoose 11 answer:\newline(A) 1.15p 1.15 p \newline(B) p1.15 \frac{p}{1.15} \newline(C) (1.05)(1.1)p (1.05)(1.1) p \newline(D) p(1.05)(1.1) \frac{p}{(1.05)(1.1)}

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Q. Daniela has a three-season acting contract for a new TV show. Her pay for Season 11 is p p dollars. Then, her pay will increase by 55 percent from Season 11 to Season 22 and by 1010 percent from Season 22 to Season 33. Which of the following represents Daniela's Season 33 pay in terms of p p ?\newlineChoose 11 answer:\newline(A) 1.15p 1.15 p \newline(B) p1.15 \frac{p}{1.15} \newline(C) (1.05)(1.1)p (1.05)(1.1) p \newline(D) p(1.05)(1.1) \frac{p}{(1.05)(1.1)}
  1. Calculate Season 22 Pay: Daniela's pay for Season 11 is pp dollars. To find her pay for Season 22, we need to increase pp by 55 percent. To calculate a 55 percent increase, we multiply pp by 1.051.05 (since 55 percent is 0.050.05 and adding this to 11 gives us the total amount after the increase).\newlineSeason 22 pay = p×1.05p \times 1.05
  2. Calculate Season 33 Pay: Next, we need to calculate the pay for Season 33, which is a 1010 percent increase from Season 22. To calculate a 1010 percent increase, we multiply the Season 22 pay by 1.101.10 (since 1010 percent is 0.100.10 and adding this to 11 gives us the total amount after the increase).\newlineSeason 33 pay = Season 22 pay ×1.10\times 1.10
  3. Substitute and Simplify: Substitute the expression for Season 22 pay into the equation for Season 33 pay.\newlineSeason 33 pay = (p×1.05)×1.10(p \times 1.05) \times 1.10
  4. Correct Multiplication: Now, we multiply the factors to find the expression that represents Daniela's Season 33 pay in terms of pp.Season 3 pay=p×1.05×1.10\text{Season 3 pay} = p \times 1.05 \times 1.10
  5. Correct Multiplication: Now, we multiply the factors to find the expression that represents Daniela's Season 33 pay in terms of pp.
    Season 33 pay = p×1.05×1.10p \times 1.05 \times 1.10Simplify the expression by multiplying 1.051.05 and 1.101.10.
    Season 33 pay = p×(1.05×1.10)p \times (1.05 \times 1.10)
    Season 33 pay = p×1.155p \times 1.155
  6. Correct Multiplication: Now, we multiply the factors to find the expression that represents Daniela's Season 33 pay in terms of pp.
    Season 33 pay = p×1.05×1.10p \times 1.05 \times 1.10 Simplify the expression by multiplying 1.051.05 and 1.101.10.
    Season 33 pay = p×(1.05×1.10)p \times (1.05 \times 1.10)
    Season 33 pay = p×1.155p \times 1.155 However, we need to find an answer that matches one of the given choices. Upon closer inspection, we realize that multiplying 1.051.05 by 1.101.10 does not give us 1.1551.155, but rather 1.1551.155 is the result of multiplying 1.051.05 by 1.101.10 incorrectly. The correct multiplication is:
    p×1.05×1.10p \times 1.05 \times 1.1022
    This was a math error in the previous step. The correct multiplication should give us:
    p×1.05×1.10p \times 1.05 \times 1.1022

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