Question 10 of 42intermediate🔧 ApplyNumerical2 marks

If 1/6! + 1/7! = x/8!, find x

Correct Answer

x = 64

Exercise: EXERCISE 6.2 | Q: 4 | (Page 8)
For More Understanding

Explanation

This question is similar to Example 8 in the textbook. The key is to express all factorials in terms of the smallest factorial (6!) and then simplify. Using the property that n! = n × (n-1)!, we can write 7! = 7×67 \times 6! and 8! = 8×78 \times 7 × 6!. This allows us to factor out 6! and solve for x.

Solution Steps

  1. Step 1: Express all factorials in terms of 6!. We have 7! = 7×67 \times 6! and 8! = 8×78 \times 7 × 6!

  2. Step 2: Substitute in the given equation: 1/6! + 1/(7×67 \times 6!) = x/(8×78 \times 7 × 6!)

  3. Step 3: Multiply both sides by 6! to get: 1 + 1/7 = x/(8×78 \times 7)

  4. Step 4: Simplify the left side: 1 + 1/7 = 7/7 + 1/7 = 8/7

  5. Step 5: So we have: 8/7 = x/(8×78 \times 7)

  6. Step 6: Cross multiply: 8×88 \times 8 × 7 = x × 7

  7. Step 7: Divide both sides by 7: x = 64

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