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## Sunday, February 21, 2010

### 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