Question 736930
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This problem can also be solved mentally using logic and mental arithmetic, although the mental calculations needed are not simple.<br>
If all 324 people were children, the ticket sales total would be 324($2.50) = 81($10) = $810.  (Notice the mental trick there of performing the required multiplication by dividing the 324 by 4 and multiplying the $2.50 by 4; then multiplying by 10 is easier than multiplying by 2.5.)<br>
That total of $810 is $1503-$810 = $693 short of the actual total.<br>
The difference in cost between an adult ticket and a child ticket is $7-$2.50 = $4.50.  The number of adults is then ($693)/($4.50) = ($1386)/($9) = 154. (Notice again the trick of making the division easier by doubling both numbers, since dividing by 9 is easier than dividing by 4.5).<br>
So the number of adults is 154 and the number of children is 324-154 = 170.<br>
ANSWER: 154 adults and 170 children<br>