Question

Venus and her cousin Ursula recently celebrated their birthdays on the same Sunday in December 2021. Ursula is now four times as old as Venus was when Ursula was the same age as Venus is now. Venus is a teenager. How old are Venus and Ursula? On which day of the week was Venus born?​

Answer 1

The date are given by the expressing the given information as functions,

and evaluating based on the constraints.

Response:

• Venus is 15 years, and Ursula is likely 24 years old

• Venus is likely born on a Thursday

How can the ages and date of birth be calculated?

Let x represent the number of years age when Ursula's age was the

same as Venus's age now and let y represent the age of Venus, we

have;

Ursula's age = y + x = 4 × (y - x)

y > 12

Which gives;

y + x = 4 × (y - x) = 4·y - 4·x

y + x = 4·y - 4·x

5·x = 3·y

$y = \dfrac{5}{3} \cdot x$

y, and x are whole numbers,  which gives;

When x = 9

• $Venus's \ age \ y = \dfrac{5}{3} \times 9 \, years =\underline{ 15 \, years}$

• Ursula's age = 15 years + 9 years = 24 years

From the calendar, we have;

Sundays in December 2021 includes the 7th, 14th, 11st and 28th of

December

The year Venus is born = 2021 - 15 = 2006 Calendar

7th, 14th, 11st and 28th of December 2006 are on Thursdays

Therefore;

• Venus was born on a Thursday

Learn more about date calculations here:

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