Athletics Club
An athletics club has girl, boy and adult members. How many members does the club have?
Age
11 to 14
Challenge level
Problem
An athletics club has two types of member: junior and adult. The junior members are either boys or girls. There are $16$ more adult members than there are junior members.
The ratio of girls to boys to adults is $3:4:9$.
In total, how many members does the club have?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 128
$$\overbrace{\text{girls} : \text{boys} }^{\text{juniors}}: \text{adults}\\
\underbrace{\hspace{2mm}3\hspace{4mm}:\hspace{4mm} 4\hspace{2mm}}\hspace{2mm} :\hspace{2mm} 9\hspace{4mm}\hspace{3mm}\\
\hspace{3mm}7\hspace{12mm}:\hspace{2mm}9\\
\hspace{4mm}\\
\text{difference} = 16 \hspace{4mm}\\
\hspace{4mm}\\
2 \text{ parts} = 16\\
1 \text{ part} = 8\\
7 \text{ parts} = 56\\
9 \text{ parts} = 72\\
56 + 72 = 128$$