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Mark is x years and Paul is 5 times Mark's age. In eight years' time, Paul will be three times as old as Mark. Form an equation in x and solve it to find Paul's and Mark's present ages.



Answer :

mathstudent55

Answer:

Presently, Mark is 8 years old, and Paul is 40 years old.

Step-by-step explanation:

Now:

Mark's age is x

Paul's age is 5x

In 8 years:

Mark's age will be x + 8

Paul's age will be 5x + 8

In 8 years, Paul will be 3 times as old as Mark.

5x + 8 = 3(x + 8)

5x + 8 = 3x + 24

2x = 16

x = 8

5x = 5 × 8 = 40

Answer: Presently, Mark is 8 years old, and Paul is 40 years old.

Check:

In 8 years, Mark will be 16, and Paul will be 48.

48/16 = 3

In 8 years, Paul will be 3 times as old as Mark as the problem states.

The answer above is correct.

Mark's present age is 8 years, and Paul's present age is 40 years.

  • Let's define the ages:
    Mark is [tex]x[/tex] years old and Paul is 5 times Mark's age, so Paul is [tex]5x[/tex] years old.
  • In 8 years:
    Mark will be[tex]x + 8[/tex] years old, and Paul will be [tex]5x + 8[/tex] years old.
  • At that time, Paul will be three times as old as Mark, so
    [tex]5x + 8 = 3(x + 8)[/tex]

Now, let's solve the equation step-by-step:

  • Expand the right-hand side:
    [tex]5x + 8 = 3x + 24[/tex]
  • Subtract [tex]3x[/tex] from both sides:
    [tex]2x + 8 = 24[/tex]
  • Subtract [tex]8[/tex] from both sides:
    [tex]2x = 16[/tex]
  • Divide both sides by[tex]2[/tex]:
    [tex]x = 8[/tex]

So, Mark is 8 years old. Paul is 5 times Mark's age, so Paul is 40 years old.

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