Question

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?

Answer 1

Answer:

40

Step-by-step explanation:

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

Answer 2

A ratio shows us the number of times a number contains another number. The number of pensioners in the sample is 40.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

Given that the ratio of children to adult visitors is 1:2. And the ratio of adults to pensioners is 3:4. Therefore, the ratio of children to pensioners will be,

Children : Pensioner = 1/2 × 3/4 = 3/8

Also, Children : Adult = 1/2 × 3/3 = 3/6

Thus, the ratio of children to adults to pensioners is 3 : 6: 8.

Now, since the sample size is 85. We can write from the ratio,

3x + 6x +  8x = 85

17x = 85

x = 5

Further, the number of pensioners in the sample is,

Number of pensioners = 8x

                                       = 8 × 5

                                       = 40

Hence, the number of pensioners in the sample is 40.

Learn more about Ratios:

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