An opening for a movie, every 12th person gets a free ticket, every 15th person gets free popcorn. How many people get both prizes?(please show work)
How many people attend the movie?
The persons getting a free ticket would be numbers 12,24,36,48,60,72,...
the persons getting free popcorn would be
numbers 15,30,45,60,75,...
isn't 60 the LCM of 12 and 15?
so the people getting both would be number
60,120,...
So, Ms. Sue pointed out, we would have to know how many people attended to answer the question.
I am sure you can take it from here.
To find the number of people who get both prizes, we need to determine the least common multiple (LCM) of 12 and 15.
Step 1: Find the multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Step 2: Find the multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, ...
As we can see, the first common multiple of 12 and 15 is 60. Therefore, every 60th person will receive both prizes.
To calculate the number of people who receive both prizes, we need to divide the total number of people by 60, as every 60th person gets both prizes. However, we need to make sure we are not counting partial groups, so we will round down.
Let's assume there are 1000 people attending the movie:
Number of people receiving both prizes = (Total number of people) / (Common multiple)
= 1000 / 60
= 16.66 (rounded down to 16)
Therefore, 16 people will receive both the free ticket and free popcorn.