MathBrush
←  All problems

Question P6 An average is a total

Today’s problem — free all day, every step. Every day has one.

Four cousins — the mean age

The mean age of four cousins is 12 years. Three of the cousins are 9, 13, and 15 years old. Find the age of the fourth cousin.

See all 6 steps

MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.

I have a code → See a free one like it

65 worked examples are free without a code, two from every pattern. No account, either way.

About this method

An average is a total

Turn the average back into a total before doing anything with it.

In this one. An average is the total shared equally, so multiply the mean by the number of cousins to recover the total, then subtract the known ages.

What you are given5 children, average 6each6 sweets each — an average, so nothing can be added yetWhat you work withtotal = 5 × 6 = 30the total30 sweets — this can be split and added

How to spot it

The word 'average' appears alongside a group being split into two parts, or two separate journeys or trips being combined into one overall figure.

Common mistake

Children average two averages directly, such as averaging two speeds or two group averages, without weighting by how many, or how long, each part actually covers.

Practise a similar question

Standard A bakery recorded its sales over 5 days: $42, $48, $55, $51 and $44. What was the average daily sales amount over the 5 days?
All 23 with this pattern →
Get the free patterns and skills booklet

Patterns and skills booklet

Worked examples of all 33 patterns and skills, in a booklet you can print.