Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q18

Ace Drama Company sold some tickets for a children's performance. It sold the same number of $8 and $5 tickets in Week 1 and collected a total of $1664. In Week 2, it sold 96 $8 and $5 tickets. If the company collected $632 more from the sale of $8 tickets than the $5 tickets in the two weeks, how many $8 tickets were sold altogether?

Solution

Week 1
$8 tickets --> 8 units
$5 tickets --> 5 units
Total 13 units --> $1664
1 unit --> $1664 divided by 13 = $128

Value of tickets sold in Week 1
$8 tickets --> 8 x $128 = $1024
$5 tickets --> 5 x $128 = $640

Difference between $8 tickets and $5 tickets in Week 1
$1024 - $640 = $384

Difference between $8 tickets and $5 tickets in Week 2
$632 - $384 = $248

If 96 tickets in Week 2 were equally sold between $5 tickets and $8 tickets, there will be 48 tickets each.
$5 tickets --> 48 x $5 = $240
$8 tickets --> 48 x $8 = $384

Difference between $8 tickets and $5 tickets in Week 2 if equal number of $5 tickets and $8 sold, would be
$384 - $240 = $144

But the difference is $248 and not $144. Instead, we have,
$248 - $144 = $104 (more)

For every $8 sold instead of $5, there would be an increase of ($8 + $5) = $13
$104 (more) divided by $13 = 8 (tickets more)

48 tickets + 8 tickets (more) = 56 $8 tickets sold on 2nd day.
1st Week --> $1024 divided by $8 = 128 (tickets)

Total number of $8 tickets
--> 128 + 56 = 184

Answer: 184 $8-tickets

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