Question 7 of 19intermediate🔧 ApplyNumerical2 marks

One quarter of a number increased by 9 gives the same number. What is the number?

Correct Answer

Step 1: Let the number = nn Step 2: Form equation: n4+9=n\frac{n}{4} + 9 = n Step 3: Subtract n4\frac{n}{4} from both sides: 9=n−n49 = n - \frac{n}{4} Step 4: Simplify: 9=3n49 = \frac{3n}{4} Step 5: Multiply by 4: 36=3n36 = 3n Step 6: Divide by 3: n=12n = 12

Answer: The number is 12. One quarter of 12 is 3, and 3 + 9 = 12, which equals the original number.

Exercise: Figure it Out (Section 2) | Q: 5 | (Page Page 17)
For More Understanding

Explanation

Let the number be nn. One quarter of the number increased by 9 equals the number itself: n4+9=n\frac{n}{4} + 9 = n. Subtracting n4\frac{n}{4} from both sides: 9=n−n4=3n49 = n - \frac{n}{4} = \frac{3n}{4}. Multiplying by 4 and dividing by 3: n=12n = 12.

Solution Steps

  1. Step 1: Let the number = nn

  2. Step 2: Form equation: n4+9=n\frac{n}{4} + 9 = n

  3. Step 3: Subtract n4\frac{n}{4} from both sides: 9=n−n49 = n - \frac{n}{4}

  4. Step 4: Simplify: 9=3n49 = \frac{3n}{4}

  5. Step 5: Multiply by 4: 36=3n36 = 3n

  6. Step 6: Divide by 3: n=12n = 12

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