1. Tickets for a film show were sold at ¢4,000 per adult and $2000 per child. The total amount raised from the 500 tickets sold was $1,600,000. i) Find the number of a) Adults who bought tickets for the show. b) Children who bought tickets for the show. ii) 12% of the amount realized was paid as tax and 2% of the amount realized was paid to the ticket sellers. Find the amount paid a) as tax. b) To the ticket sellers. 2. Ama’s age is two-thirds that of her elder sister. Four years ago Ama’s age was half the sister’s. How old is her sister?
Answers
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Let the number of adults be X , therefore number of children are 500 -X.
(i) (a) $4000 × X + $2000 × (500-X) = $1600,000
$4000X + $1,00,0000 - $2000X= $1600,000
$2000X + $1,00,0000 = $1600,000
$2000X = $600,000
X = 600000/2000 = 300 Adults
(b) 500 tickets - 300 tickets = 200 children
(ii) (a) 12% of $1600,000
= $192000 paid as tax.
(b) 2% of $1600,000
=$32000
Let the age of elder sister be X.
Ama's age is 2/3 rd of X.
Sister's age 4 years ago was X-4
4 years ago Ama's age was 1/2 of (X-4).
Therefore , 2/3X - 4 = 1/2 of (X-4)
= 2(2X-12) = 3(X-4)
= 4X - 24 = 3X - 12
= X = 12 years
Hence, her sister is 12 years old.