Question 13 of 17intermediate🔧 ApplyNumerical3 marks

A mother is 5 times her daughter's age. In 6 years' time, the mother will be 3 times her daughter's age. How old is the daughter now?

Correct Answer

Step 1: Let dd = daughter's current age.

Step 2: Mother's current age = 5d5d.

Step 3: In 6 years: daughter = d+6d + 6, mother = 5d+65d + 6.

Step 4: Equation: 5d+6=3(d+6)5d + 6 = 3(d + 6).

Step 5: Solve:

5d+6=3d+185d + 6 = 3d + 18 2d=122d = 12

Step 6: Therefore d=6d = 6 years.

Answer: The daughter is 6 years old now.

Exercise: Figure it Out (Section 3) | Q: 7 | (Page Page 12)
For More Understanding

Explanation

Using algebra: Let d = daughter's current age. Mother's current age = 5d. In 6 years: daughter will be d + 6, mother will be 5d + 6. Given that mother will be 3 times daughter's age: 5d + 6 = 3(d + 6). Solving: 5d + 6 = 3d + 18, so 2d = 12, giving d = 6.

Solution Steps

  1. Step 1: Let d = daughter's current age

  2. Step 2: Mother's current age = 5d

  3. Step 3: In 6 years: daughter = d + 6, mother = 5d + 6

  4. Step 4: Equation: 5d + 6 = 3(d + 6)

  5. Step 5: Solve: 5d + 6 = 3d + 18, so 2d = 12

  6. Step 6: Therefore d = 6 years

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