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On Saturday, some adults and some children were in a theatre - Edexcel - GCSE Maths - Question 2 - 2017 - Paper 2
Question 2
On Saturday, some adults and some children were in a theatre. The ratio of the number of adults to the number of children was 5 : 2. Each person had a seat in the C... show full transcript
Worked Solution & Example Answer:On Saturday, some adults and some children were in a theatre - Edexcel - GCSE Maths - Question 2 - 2017 - Paper 2
Step 1
Determine the total number of children.
Answer
Let the number of children be ( x ). According to the problem, ( \frac{3}{4} ) of these children had seats in the Stalls, meaning ( \frac{1}{4} ) did not have seats. Since 117 children had seats in the Circle, we can set up the equation:
[ \frac{1}{4} x + 117 = x ]
Solving for ( x ):
[ \frac{1}{4} x = x - 117 ] [ \frac{1}{4} x = \frac{4}{4} x - 117 ] [ (1 - \frac{1}{4}) x = 117 ] [ \frac{3}{4} x = 117 ] [ x = 117 \times \frac{4}{3} = 156 ]
Thus, there are 156 children in total.
Step 2
Calculate the number of adults.
Answer
The ratio of adults to children is 5:2. If there are 156 children, we can find the number of adults, ( y ), using the ratio:
[ \frac{y}{156} = \frac{5}{2} ]
Cross-multiplying:
[ 2y = 5 \times 156 ] [ 2y = 780 ] [ y = \frac{780}{2} = 390 ]
Therefore, there are 390 adults.
Step 3
Calculate total people and check seat occupancy.
Answer
The total number of people in the theatre is:
[ 156 + 390 = 546 ]
To determine the percentage of seat occupancy:
[ \text{Occupancy} = \frac{546}{2600} \times 100 \approx 21 ext{.}0% ]
Since 21.0% is less than 60%, there were not more than 60% of the seats occupied.