Question

On Saturday, some adults and some children were in a theatre.
The ratio of the number of adults to the number of children was 7:2
Each person had a seat in the Circle or had a seat in the Stalls.
of the children had seats in the Stalls.
124 children had seats in the Circle.
There are exactly 3875 seats in the theatre.
On this Saturday, what percentage of the seats had people sitting on them?
+
Total marks: 5

Answer 1

The ratio of adults indicates that there are 7 adults foe every 2 children,

given the number of children, the number of people can be found.

• The percentage of seats that had people sitting on them is 72%

Reasons:

The given parameters are;

Ratio of adults to children = 7 : 2

The proportion of children that had sit in the stalls = 4/5

Number of children that had sit in the Circle = 124 children

Number of seats at the theater = 3,875

Required:

The percentage of the sits that had people sitting on them.

Solution:

Let x represent the number of children, we have;

Number of children in the stalls = $\displaystyle \frac{4}{5} \cdot x$

$\displaystyle Number \ of \ children \ in \ the \ circle = \mathbf{x - \frac{4}{5} \cdot x} = 124$

Therefore;

$\displaystyle x=\frac{124}{1 - \frac{4}{5} \times 1} = \mathbf{620}$

The number of children, x = 620 children

• $\displaystyle \mathbf{ \frac{Number \ of \ adult}{Number \ of \ children}} = \frac{7}{2}$

Therefore;

$\displaystyle \frac{Number \ of \ adult}{620} = \frac{7}{2}$

2 × Number of adults = 7 × 620

Number of adults = 7 × 620 ÷ 2 = 2,170

The total number of persons, n = Number of children + Number of adults

Therefore;

n = 2,170 + 620 = 2,790

$\displaystyle Percentage \ of \ sits \ with \ people = \mathbf{ \frac{2,790}{3,875} \times 100} = \underline{72 \%}$

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