The average age of grandpa, grandma, and their five grandchildren is 26 years. The average age of the grandchildren themselves is 7 years. Grandma is one year younger than grandpa.

How old is grandma?

(L. Hozová)

Hint. How old are all the grandchildren together?
The grandchildren together are 35 years old $(5 \cdot 7=35)$. Grandpa, grandma, and the grandchildren together are 182 years old $(7 \cdot 26=182)$. Therefore, grandpa and grandma together are 147 years old $(182-35=147)$.

The average age of grandma and grandpa is 73 and a half years $(147: 2=73.5)$, and grandma is one year younger than grandpa. Therefore, grandma is 73 years old (and grandpa is 74 years old; 73.5 $\pm 0.5$ ).

Note. If $b$ represents grandma's age and $d$ represents grandpa's age, then the information from the problem can be written as

$$
(d+b+5 \cdot 7): 7=26, \quad d=b+1
$$

From the first equation, we get $d+b=26 \cdot 7-5 \cdot 7=21 \cdot 7=147$. Substituting the second equation, we get $2b+1=147$, so $b=(147-1): 2=73$.