The admission tickets for children to watch a magic show were fixed on all days of a week. On Thursday, there were 80 boys and 60 girls at the show. On Friday, the number of boys increased by 30% and the number of girls decreased by 15%. Altogether, $9440 was collected from the sale of admission tickets over the two days.

  1. (a)

    What was the price of each admission ticket?

    Ans : (a) ___

  2. (b)

    What was the percentage increase in the number of tickets sold from Thursday to Friday?

    Ans : (b) ___

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Worked solution

13(a)

1. Calculate the number of boys and girls who attended the show on Friday.

Number of boys on Friday = 80×(1+0.30)=80×1.3=10480 \times (1 + 0.30) = 80 \times 1.3 = 104
Number of girls on Friday = 60×(1−0.15)=60×0.85=5160 \times (1 - 0.15) = 60 \times 0.85 = 51

2. Find the total number of tickets sold over the two days.

Tickets sold on Thursday = 80+60=14080 + 60 = 140
Tickets sold on Friday = 104+51=155104 + 51 = 155
Total tickets sold = 140+155=295140 + 155 = 295

3. Calculate the price of each admission ticket.

Price per ticket = $9440÷295=$32\char36{}9440 \div 295 = \char36{}32

Answer

$32

13(b)

1. Find the total number of tickets sold on Thursday.

Total tickets on Thursday = 80+60=14080 + 60 = 140

2. Find the number of boys and girls who attended on Friday.

Number of boys on Friday = 80×(1+0.30)=80×1.3=10480 \times (1 + 0.30) = 80 \times 1.3 = 104
Number of girls on Friday = 60×(1−0.15)=60×0.85=5160 \times (1 - 0.15) = 60 \times 0.85 = 51

3. Calculate the percentage increase in the total number of tickets sold.

Total tickets on Friday = 104+51=155104 + 51 = 155
Increase in tickets = 155−140=15155 - 140 = 15
Percentage increase = 15140×100%=328×100%=757%=1057%\frac{15}{140} \times 100\% = \frac{3}{28} \times 100\% = \frac{75}{7}\% = 10\frac{5}{7}\%

Answer

1057%10\frac{5}{7}\%

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