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Alphonse is x years old and Beatrice is y years old. Three times Alphonse’s age is five times Beatrice’s age. Twice more than Beatrice’s age is four more years than Alphonse’s age. How old is Alphonse and Beatrice

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mhanifa

Answer:

  • Alphonse is 20 and Beatrice is 12 years old

Step-by-step explanation:

Set up equations as below

Three times Alphonse’s age is five times Beatrice’s age

⇒ 3x = 5y

Twice more than Beatrice’s age is four more years than Alphonse’s age

⇒ x + 4 = 2y

Solve the system by substitution

  • x = 2y - 4 ⇒ 3x = 3(2y - 4) = 6y - 12
  • 6y - 12 = 5y
  • 6y - 5y = 12
  • y = 12

Find the value of x

  • x = 2*12 - 4 = 24 - 4 = 20

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