# Candy Bars

A rich old lady decided to give 12 candy bars to each of the girls in her town and 8 candy bars to each of the boys. Of the 612 children in her town, only half the girls and three quarters of the boys were allowed to take the candy bars. How many candy bars did the rich old lady have to buy?

### 4 guesses to Candy Bars

• nikki

4131

• Dude

No, but keep trying.

• Roolstar

Easy way:
Take any distribution of kids
600 girls and 12 boys => 150*12 + 9*8 = 3672 candy bars
608 girls and 4 boys => 154*12 + 3*8 = 3672 candy bars
600 Boys and 12 Girls => 450*8 + 6*12 = 3672

Global Method:
8 candy bars for 3/4 of the boys means 6 candy bars for all boys
12 candy bars for 1/2 of the girls means 6 candy bars for all girls
=> 6 candy bars for all children => 612*6 = 3672

• Dude

3,672 is correct!

The actual number of girls and boys doesn’t actually matter!
If all of the children were girls then half of them (306) would be given 12 candy bars:

306 x 12 = 3672

If all of the children were boys then three quarters of them (459) would be given 8 candy bars:459 x 8 = 3672

If there were 512 girls (so 256 would get 12 candy bars = 3072) and 100 boys (so 75 would get 8 candy bars = 600):

256 x 12 + 75 x 8 = 3672

We can change the numbers of girls and boys, but it doesn’t change the answer. The reason for this lies in the fact that 1/2 girls x 12 candy bars = 3/4 boys x 8 candy bars (both are 6).

Great job, you are today’s winner.