Concepts addressed: systems of equations, date calculation.
Recommended grade: 8th.
Difficulty level: Basic.
An advanced version of Witty sister is also available.
You’re visiting your friend at their house, and are soon approached by their little sister. She’s recently taken to riddles, and she can’t wait to tell you her recent one.
- With a grin on her face, she recites, “Me and my mum have 50 years between us, and if you triple my age and take it away from my mum’s, you’ll get 14 years. How old are we?” Unfortunately, your friend went out for a second, so you can’t just ask him.
- The sister promises you a reward for the right answer – a candy bar! She’s been eating one of those every week this year with the first one eaten on New Year’s Day. How much sugar has she consumed with those candy bars alone, if each contains 1.2 oz?
- Date calculator – https://www.omnicalculator.com/everyday-life/date
Question 1 hints:
Question 2 hints:
Solutions (WARNING: depend on the date, example for March 25th, 2020):
The next sentence tells us that if we take the girl’s age, which for us is y, multiply it by 3 and subtract it from the mother’s age, which is x, then we’ll get 14 years. Again, to write this correspondence algebraically, we can say that x – 3 * x = 14.
This way, we obtain a system of two equations with two variables:
x + y = 50,
x – 3y = 14.
To find its solution let us subtract the second one from the first, i.e., we write
x + y – (x – 3y) = 50 – 14,
4y = 36.
After dividing both sides by 4, we obtain y = 9. Now we can substitute that value to the first of the initial equations, which gives
x + 9 = 50.
Lastly, we move the 9 to the right side, remembering to change its sign:
x = 50 – 9 = 41.
This means that the mother is x = 41, and the daughter is y = 9.