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Algebra · age expressions

P6 · Algebra · PSLE Maths

Question

Raju is x years old now. His sister, Siti, is 4 years younger than him. What is the sum of their ages in 6 years' time? Express your answer in terms of x. If x = 15, what will the sum of their ages be in 6 years' time?

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Hint

Write each person's age now first, then add 6 years to each person.

Show the answer and step-by-step explanation

Answer: Sum of ages in 6 years 2x+8; When x = 15 38 years

  1. Draw ages now — Raju is x years old now. Siti is 4 years younger, so Siti is x - 4 years old now.
  2. Difference of 4 — The difference between the two bars shows that Siti is 4 years younger than Raju. The age difference is 4 years now.
  3. After 6 years — In 6 years' time, both of them will be 6 years older. So add 6 to Raju and add 6 to Siti.
  4. Simplify — Siti's age: x - 4 + 6 = x + 2. Now add their ages in 6 years' time.
  5. Substitute — When x = 15, substitute 15 into the expression: 2 × 15 + 8 = 38. 📌 Key idea: express the ages now, add the same number of years to each person, simplify, then substitute.

Method: For algebra age problems, use x to express the ages now. After some years, add the same number of years to each person, simplify like terms, then substitute the value of x.

Practice: 3 similar questions

  1. Ali is y years old now. His sister, Siti, is 2 years younger than him. What is the sum of their ages in 4 years' time? Express your answer in terms of y. If y = 10, what will the sum be in 4 years' time?
    Answer

    0, 26 years — Siti is y - 2 years old now. In 4 years' time: Ali will be y + 4, and Siti will be y - 2 + 4 = y + 2. Sum of ages = y + 4 + y + 2 = 2y + 6. When y = 10, 2 × 10 + 6 = 26 years.

  2. Mei Ling is a years old now. Her brother, Raju, is 5 years older than her. What is the sum of their ages in 3 years' time? Express your answer in terms of a. If a = 12, what will the sum be in 3 years' time?
    Answer

    0, 35 years — Raju is a + 5 years old now. In 3 years' time: Mei Ling will be a + 3, and Raju will be a + 5 + 3 = a + 8. Sum of ages = a + 3 + a + 8 = 2a + 11. When a = 12, 2 × 12 + 11 = 35 years.

  3. Raju is x years old now. His sister, Siti, is 5 years younger than him. Their cousin, Mei Ling, is 3 years younger than Siti. What is the sum of their ages in 4 years' time? Express your answer in terms of x. If x = 14, what will the sum be in 4 years' time?
    Answer

    0, 41 years — Raju is x years old now; Siti is x - 5 years old now. Mei Ling is 3 years younger than Siti, so she is x - 5 - 3 = x - 8 years old now. In 4 years' time: Raju will be x + 4, Siti will be x - 1, and Mei Ling will be x - 4. Sum of their ages = x + 4 + x - 1 + x - 4 = 3x - 1. When x = 14, 3 × 14 - 1 = 41 years.

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