Question

Allison's cinema has 100 seats. One day, Allison notices that her cinema is full, and she has taken exactly £100. The prices where: adult=£3.50, pensioner= £1, child=£0.85. she knows not everyone in the audience is a pensioner. Howmmany adults, children and pensioners where there?

Answer 1

Answer:

So starting with what we already know, £100 was paid in all, all 100 seats were taken. Adults pay £3.50, Children pay $0.85 and the Pensioners pay $1.00. I basicaly started off by trying it so all adults, children and pensioners are the exact same number. 33 adult tickets would cost them £115.50. Crossing that suggestion out; I tried again, but this time, with 3 adults, 50 children and the 47 that were left, i put as pensioners. So, now there is 100 people and this is kind of working out:

3 adults= £10.50, 50 children= £42.50, 47 pensioners= £47.00 Total £100

Step-by-step explanation:

Answer 2

As per the given data number of adults $=3$ , number of children $= 50$ and number of pensioner $= 47$.

What is number?

" Number is defined as the count of the given quantity."

According to the question,

Total number of seats $=100$

Total amount of full seats $= \£100$

Price of adult ticket $= \£ 3.50$

Price of children ticket $= \£ .85$

Price of adult ticket $= \£ 1$

$'x'$represents the number of adults

$'y'$ reprsents the number of children

$'z'$ represents the number of pensioner

As per given condition we have,

$x + y + z = 100\\\\\£3.50x + \£0.85y + \£1z = \£ 100$

Using trial and error method we get,

$x = 3 ,\\\\y= 50\\\\z= 47$

For total number of  tickets

$3 + 50 + 47 = 100$

Left hand side = Right hand side

Substitute in left hand side of total cost we get,

$\£3.50(3) + \£0.85(50) + \£1(47) \\\\= \£10.50 + \£42.50 + \£47$

$= \£ 100$

= Right hand side

Hence, as per the given data number of adults $=3$ , number of children $= 50$ and number of pensioner $= 47$.

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