Question

Katya cut part of the jump rope off to make it shorter. The new length is 8 and StartFraction 1 over 6 EndFraction feet. The difference between the original length and the new length is StartFraction 5 over 6 EndFraction foot. The equation x minus 8 and StartFraction 1 over 6 EndFraction = StartFraction 5 over 6 EndFraction can be used to represent this problem, where x is the original length of the rope. What was the original length of the rope?

7 and one-thirdfeet
8 and two-thirdsfeet
9 feet
10 feet

Answer 1

Step-by-step explanation: To find the original length of the rope, we can solve the equation x - 8 1/6 = 5/6, where x represents the original length.

To solve the equation, we need to isolate x on one side of the equation. Let's begin by adding 8 1/6 to both sides:

x - 8 1/6 + 8 1/6 = 5/6 + 8 1/6

Simplifying, we get:

x = 5/6 + 8 1/6

Next, we need to convert the mixed number 8 1/6 to an improper fraction. To do this, we multiply the whole number (8) by the denominator (6) and add the numerator (1). This gives us:

8 × 6 + 1 = 48 + 1 = 49

So, 8 1/6 is equivalent to 49/6.

Substituting this value back into the equation, we have:

x = 5/6 + 49/6

To add the fractions, we need a common denominator, which is 6. So, we rewrite the equation as:

x = (5 + 49)/6

Adding the numerators, we get:

x = 54/6

Simplifying the fraction, we divide the numerator by the denominator:

x = 9

Therefore, the original length of the rope was 9 feet.

The correct answer is:

9 feet