11 Plus Exams Forum

The ages of Grandma, Aunt Jane and Sara add up to 119 years. Grandma is twice as old as Aunt Jane, and Aunt Jane is twice as old as Sara.
Grandma is years old, Aunt Jane years old and Sara is years old.


The answer is 17, 34 and 68

But how shall we do the calculation

Please help

Grandma is twice as old as Aunt Jane, and Aunt Jane is twice as old as Sara.

So, trying to avoid using algebra, think about each person's age in terms of Sara's.

Aunt Jane = two Sara

Grandma = two Aunt Jane = .... Sara

Then we know the total, so add them all up.

I do not agree with posting full solutions as that won't help you another time.

I would do it like this:
Sara is the youngest, so call her age X years
Aunt Jane is twice Sara's age, i.e. 2X
Grandma is twice Aunt Jane's age, i.e. 4X

Total of ages: X + 2X + 4X = 7X
7X = 119
X = 119/7 = 17

It's better for the OP if full solutions are not posted ...

I would bar model. The strips are a stunning aid in proportional reasoning questions. Hard to communicate on here, but quick and simple to draw and give children a visual aid and no need for algebra.

Start with Sara and draw a block.
---
Then draw two blocks the same size, Jane.
------|---
Next draw two Jane sized blocks (4 Sara blocks).
------|------|---|---|---
You now have one strip comprised of 7 Sara sized blocks. The total ages are the whole strip, so divide by 7 to give Sara.