Preet is 6 years older than Abdul. Six years ago, Preet's age was four times Abdul's age. Find their present ages.

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Understand the Problem

We need to determine the current ages of Preet and Abdul based on two pieces of information: Preet is currently 6 years older than Abdul, and six years ago, Preet's age was four times Abdul's age at that time. This can be solved using a system of equations.

Answer

Preet is 14 years old and Abdul is 8 years old.
Answer for screen readers

Preet is 14 years old and Abdul is 8 years old.

Steps to Solve

  1. Define variables

Let $P$ be Preet's current age and $A$ be Abdul's current age.

  1. Write the first equation

Preet is 6 years older than Abdul, so we have the equation:

$$P = A + 6$$

  1. Write the second equation

Six years ago, Preet's age was $P - 6$ and Abdul's age was $A - 6$. Preet's age was four times Abdul's age at that time, so we have the equation:

$$P - 6 = 4(A - 6)$$

  1. Simplify the second equation

Expand and simplify the second equation:

$$P - 6 = 4A - 24$$

$$P = 4A - 18$$

  1. Solve the system of equations

Since $P = A + 6$ and $P = 4A - 18$, we can set the two expressions for $P$ equal to each other:

$$A + 6 = 4A - 18$$

  1. Solve for $A$

Subtract $A$ from both sides:

$$6 = 3A - 18$$

Add 18 to both sides:

$$24 = 3A$$

Divide by 3:

$$A = 8$$

  1. Solve for $P$

Substitute the value of $A$ into the first equation $P = A + 6$:

$$P = 8 + 6$$

$$P = 14$$

  1. State the present ages

Preet's current age is 14 years old and Abdul's current age is 8 years old.

Preet is 14 years old and Abdul is 8 years old.

More Information

We can check our answer. Preet is indeed 6 years older than Abdul ($14 = 8 + 6$). Six years ago, Preet was $14 - 6 = 8$ years old and Abdul was $8 - 6 = 2$ years old. Preet's age (8) was four times Abdul's age (2) at that time ($8 = 4 \times 2$).

Tips

A common mistake is setting up the equations incorrectly, particularly the second equation involving their ages six years ago. Students might forget to subtract 6 from both Preet's and Abdul's current ages before applying the four times relationship. They might write $P = 4A - 6$ or $P - 6 = 4A$ which are incorrect. Another common mistake is an arithmetic error when solving the system of equations.

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