Question 14 of 49intermediate🔧 ApplyNumerical3 marks

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

Correct Answer

Shorter piece = 60 feet, Longer piece = 240 feet

Exercise: Exercise Set 2.2 | Q: 6 | (Page 6)
For More Understanding

Explanation

The problem requires setting up a linear equation based on the given conditions. By defining the shorter piece as a variable and expressing the longer piece in terms of that variable, we can use the total length of the fence to solve for the unknown.

Solution Steps

  1. Step 1: Let the length of the shorter piece be xx feet. Since the longer piece is four times as long, the longer piece is 4x4x feet.

  2. Step 2: The total length of the fence is 300 feet. Therefore, we form the equation: x+4x=300x + 4x = 300.

  3. Step 3: Simplifying the equation gives 5x=3005x = 300. Dividing both sides by 5, we get x=60x = 60.

  4. Step 4: The shorter piece is x=60x = 60 feet, and the longer piece is 4x=4×60=2404x = 4 \times 60 = 240 feet.

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