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The team needs to create a deck that spans the entire length from one side of the lake to the other. The deck consists of one center plank and two side planks. Each side plank is the same length.

- Total length of the deck: 150 feet
- Length of the center plank: 97 1/3 feet

What is the length, in feet, of each side plank? Show your work.

Answer :

Each side plank is 52 2/3 feet long. Total deck length is 150 feet, with a center plank of 97 1/3 feet.

To find the length of each side plank, we can start by subtracting the length of the center plank from the total length of the deck.

Total length of the deck = 150 feet

Length of the center plank = 97 1/3 feet

So, the length of each side plank can be calculated as follows:

Total length of both side planks = Total length of the deck - Length of the center plank

Let's solve this step by step:

1. Convert 97 1/3 feet to an improper fraction:

[tex]\(97 \frac{1}{3} = \frac{97 \times 3}{3} + \frac{1}{3} = \frac{291}{3} + \frac{1}{3} = \frac{292}{3}\)[/tex]

2. Subtract the length of the center plank from the total length of the deck:

[tex]\(150 - \frac{292}{3}\)[/tex]

3. Convert 150 to a fraction with the same denominator as [tex]\( \frac{292}{3}\)[/tex]:

[tex]\(150 = \frac{150 \times 3}{3} = \frac{450}{3}\)[/tex]

Now, we can subtract the fractions:

[tex]\( \frac{450}{3} - \frac{292}{3} = \frac{450 - 292}{3} = \frac{158}{3}\)[/tex]

4. Finally, convert the improper fraction back to a mixed number:

[tex]\(158 \div 3 = 52 \frac{2}{3}\)[/tex]

So, each side plank is [tex]\(52 \frac{2}{3}\)[/tex] feet long.

Here's the summary of the calculations:

Total length of both side planks = Total length of the deck - Length of the center plank

[tex]\(= 150 - \frac{292}{3}\)[/tex]

[tex]\(= \frac{450}{3} - \frac{292}{3}\)[/tex]

[tex]\(= \frac{158}{3}\)[/tex]

[tex]\(= 52 \frac{2}{3}\)[/tex] feet.

26 1/2 feet is the length for each side plank.

The deck's total length is 150 feet, and the center plank's length is 97 1/3 feet.

Here's the calculation:

  • Convert 97 1/3 to an improper fraction: 97 1/3 = 291/3 feet.
  • Subtract the length of the center plank from the total length: 150 feet - 291/3 feet.
  • First, convert 150 to a fraction with a denominator of 3: 150 = 450/3 feet.
  • Now subtract the fractions: 450/3 feet - 291/3 feet = 159/3 feet.
  • This is the combined length of the two side planks. Since both side planks are of equal length, divide by 2 to find the length of one side plank: 159/3 feet \/ 2 = 159/6 feet.
  • Convert the improper fraction to a mixed number: 159/6 feet = 26 1/2 feet.

Therefore, the length of each side plank is 26 1/2 feet.

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