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 Circle or had a seat in the Stalls. \( \frac{3}{4} \) of the children had seats in the Stalls. 117 children had seats in the Circle. There are exactly 2600 seats in the theatre. On this Saturday, were there people on more than 60% of the seats? You must show how you get your answer.

GCSE Edexcel Maths Ratio Analysis and Problem Solving: On Saturday, some adults and som

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

Find the total number of children

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Answer

Let the number of adults be ( 5x ) and the number of children be ( 2x ). The total number of children can be found using the information that 117 children had seats in the Circle and that ( \frac{3}{4} ) of the children had seats in the Stalls. Thus, we can express the total number of children as follows:

[ 117 = 2x - \frac{3}{4}(2x) ]

Solving for ( x ):

[ 117 = 2x - \frac{3}{2}x \implies 117 = \frac{1}{2}x \implies x = 234 ]

So, the total number of children is ( 2x = 468 ).

Step 2

Calculate the total number of adults

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Answer

Using the value found for ( x ), the total number of adults is ( 5x = 5 \times 234 = 1170 ).

Step 3

Determine the total number of people in the theatre

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Answer

The total number of people in the theatre is the sum of the adults and children: 1170 (adults) + 468 (children) = 1638.

Step 4

Check if more than 60% of the seats were occupied

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Answer

To find out if more than 60% of the 2600 seats were occupied, calculate:

[ 0.6 \times 2600 = 1560 ]

Since 1638 exceeds 1560, we conclude that there were indeed people on more than 60% of the seats.

On Saturday, some adults and some children were in a theatre - Edexcel - GCSE Maths - Question 2 - 2017 - Paper 2

Worked Solution & Example Answer:On Saturday, some adults and some children were in a theatre - Edexcel - GCSE Maths - Question 2 - 2017 - Paper 2

Find the total number of children

Calculate the total number of adults

Determine the total number of people in the theatre

Check if more than 60% of the seats were occupied

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