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Jordan has an extension ladder that currently reaches a height of 11(3)/(5) feet. She needs the ladder to extend to a height of 15(1)/(5) feet. How much longer, in feet, does the ladder need to be extended?
(A) 3(3)/(5)
(B) 4(2)/(5)
(C) 11(4)/(5)
(D) 26(4)/(5)

Jordan has an extension ladder that currently reaches a height of 1135 11 \frac{3}{5} feet. She needs the ladder to extend to a height of 1515 15 \frac{1}{5} feet. How much longer, in feet, does the ladder need to be extended?\newline(A) 335 3 \frac{3}{5} \newline(B) 425 4 \frac{2}{5} \newline(C) 1145 11 \frac{4}{5} \newline(D) 2645 26 \frac{4}{5}

Full solution

Q. Jordan has an extension ladder that currently reaches a height of 1135 11 \frac{3}{5} feet. She needs the ladder to extend to a height of 1515 15 \frac{1}{5} feet. How much longer, in feet, does the ladder need to be extended?\newline(A) 335 3 \frac{3}{5} \newline(B) 425 4 \frac{2}{5} \newline(C) 1145 11 \frac{4}{5} \newline(D) 2645 26 \frac{4}{5}
  1. Find Height Difference: First, we need to find the difference between the desired height and the current height of the ladder.
  2. Convert to Improper Fractions: Convert the mixed numbers to improper fractions to make the subtraction easier. \newline11(35)11\left(\frac{3}{5}\right) feet is the same as (11×5+3)/5=585\left(11 \times 5 + 3\right)/5 = \frac{58}{5} feet.\newline15(15)15\left(\frac{1}{5}\right) feet is the same as (15×5+1)/5=765\left(15 \times 5 + 1\right)/5 = \frac{76}{5} feet.
  3. Subtract Heights: Subtract the current height from the desired height: (765)(585)(\frac{76}{5}) - (\frac{58}{5}) feet.
  4. Direct Numerator Subtraction: Since the denominators are the same, we can subtract the numerators directly: 7658=1876 - 58 = 18.
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  6. Final Answer Conversion: Divide 1818 by 55. The quotient is 33 with a remainder of 33. So, 185\frac{18}{5} feet is the same as 3(35)3\left(\frac{3}{5}\right) feet.

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