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Pregunta

Pasos de solución

1. Understand the question

   tips for success• read the assignment carefully and make sure you answer each part of the question or questions.• check your work when youre done.your assignmentamelia is painting her room. she has one wall left (shown in the figure) and only $\frac{1}{4}$ gallon of paint, which will cover about 100 square feet. does she have enough paint left?$11\frac{1}{2}$ feet$8\frac{1}{2}$ feet3 feet$6\frac{3}{4}$ feet1. find the area of the wall, including the door. leave your answer as an improper fraction. (2 points)height: $6\frac{1}{2}$ feet (or $\frac{13}{2}$ feet)2. find the area of the door. leave your answer as an improper fraction. (2 points)

2. Explanation

   Step1: Convert wall dimensions to improper fractions

   Wall width: $11\frac{1}{2} = \frac{23}{2}$ feet, Wall height: $8\frac{1}{2} = \frac{17}{2}$ feet

   Step2: Calculate total wall area

   $\text{Area}_{\text{wall}} = \frac{23}{2} \times \frac{17}{2} = \frac{391}{4}$ square feet

   Step3: Convert door dimensions to improper fractions

   Door width: $3 = \frac{3}{1}$ feet, Door height: $6\frac{3}{4} = \frac{27}{4}$ feet

   Step4: Calculate door area

   $\text{Area}_{\text{door}} = \frac{3}{1} \times \frac{27}{4} = \frac{81}{4}$ square feet

   Step5: Calculate area to paint

   $\text{Area}_{\text{to paint}} = \frac{391}{4} - \frac{81}{4} = \frac{310}{4} = 77.5$ square feet

   Step6: Compare to paint coverage

   Paint covers 100 square feet, $77.5 < 100$

3. Final answer
   1. $\frac{391}{4}$ square feet
   2. $\frac{81}{4}$ square feet
   3. Yes, she has enough paint left.

Respuesta

Question Analysis

OCR Text

tips for success• read the assignment carefully and make sure you answer each part of the question or questions.• check your work when youre done.your assignmentamelia is painting her room. she has one wall left (shown in the figure) and only $\frac{1}{4}$ gallon of paint, which will cover about 100 square feet. does she have enough paint left?$11\frac{1}{2}$ feet$8\frac{1}{2}$ feet3 feet$6\frac{3}{4}$ feet1. find the area of the wall, including the door. leave your answer as an improper fraction. (2 points)height: $6\frac{1}{2}$ feet (or $\frac{13}{2}$ feet)2. find the area of the door. leave your answer as an improper fraction. (2 points)

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