Concepts addressed: **systems of equations**, **date calculation**.

Recommended grade: **8th**.

Difficulty level: **Basic**.

An advanced version of Witty sister is also available.

**Scenario:**

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?

**Useful calculators:**

- 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):**

**Step-by-step solution:**

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*,

which gives*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.

I teach 8th grade math and algebra in Los Angeles, CA. I like the concept. Upon just reading the scenario, the biggest hurdle is language. About half my studnets are English Language Learners. They might know Mum is the same as Mom or figure it out quickly. They would be confused by “50 years between us”. “Consumed with those candy bars alone” is also a phrase that would be confusing. Graphics would help the candy bars.

As a teacher not having all the students use the same date for the candy bar question would be a challenge. If they are helping each other, and have started with a different date, they will get more confused. Particularly with Distance Learning they may be a week or two apart on starting the problem.

Thank you so much! Your comment on the language is really valuable to me. I introduced some changes, do you think now it’s better for an 8th grader? Also, I’d love to know what kind of a graphic you’d imagine for this problem!

“Me and my mum have 50 years between us”

I read this to mean that the difference between their ages was 50 which lead me to a different solution. Mum being 68 and the daughter being 18

Hello! Thank you for requesting my feedback on your scenarios. I am a middle school math teacher in Gibraltar, Michigan, USA. An area of strength in these scenarios is that they provide “hints”. That is very helpful to meet the needs of diverse learners. These scenarios are very good, however, if I were to utilize them in my classroom, the language would need to be rewritten in American English. My students would have a lot of questions about some of the wording. I love the way you speak and write, but they would have difficulty understanding the context of the problems.