Visitors to a cinema are either children, adults or pensioners. The ratio of children to adult visitors is 1:2. The ratio of adults to pensioners is 3:4. A stratified sample of 85 is to be taken from the cinema visitors. How many pensioners should be in the sample?

Question

Mathematics

Travis Shepherd

6 November, 19:16

Visitors to a cinema are either children, adults or pensioners. The ratio of children to adult visitors is 1:2. The ratio of adults to pensioners is 3:4. A stratified sample of 85 is to be taken from the cinema visitors. How many pensioners should be in the sample?

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Ashton Humphrey · Answer 1

p=40

c/a=1/2 so a=2*c

a/p=3/4 so 3p=4a=4*2c so p=8c/3

c+a+p=85

c+2c+8c/3=85

3c+8c/3=85 multiply by 3

9c+8c=255

17c=255

but p = 8c/3 so c=3p/8

17*3p/8=255 multiply by 8

51p=255*8=2040

p=2040/51=40