A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and a free concert ticket to every 100th caller. When will the station first give away all three prizes to one caller?
The
th caller will get all three prizes.
Question 2
When this happens, how much money and how many tickets are given away?
Amount of money given away: $
a
Number of tickets given away:
A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and a free concert ticket to every 100th caller. When will the station first give away all three prizes to one caller?
The 300300 - correctth caller will get all three prizes.
response - correct
Question 2
When this happens, how much money and how many tickets are given away?
Amount of money given away: $
To find the first time the station gives away all three prizes to one caller, we need to find the least common multiple (LCM) of the numbers 15, 25, and 100.
Prime factors of 15: 3, 5
Prime factors of 25: 5, 5
Prime factors of 100: 2, 2, 5, 5
LCM: 2 * 2 * 3 * 5 * 5 = 300
So the station will first give away all three prizes to the 300th caller.
Now, let's calculate the amount of money and the number of tickets given away:
Number of $15 prizes:
300 ÷ 15 = 20 prizes
Number of $25 prizes:
300 ÷ 25 = 12 prizes
Number of free concert tickets:
300 ÷ 100 = 3 tickets
Amount of money given away:
20 * $15 + 12 * $25 = $300 + $300 = $600
Number of tickets given away:
3 tickets
Therefore, when the station first gives away all three prizes to one caller, they will give away $600 and 3 tickets.
To find out when the station will first give away all three prizes to one caller, we need to find the lowest common multiple (LCM) of the numbers 15, 25, and 100.
First, let's find the prime factors of each number:
15 = 3 * 5
25 = 5 * 5
100 = 2 * 2 * 5 * 5
The LCM is the product of the highest power of each prime factor that appears in any of the given numbers. In this case, since the prime factor 5 appears twice in 100, we include it with the highest power, and for the factor 2, since it appears only once in 100, we include it as well:
LCM = 2 * 2 * 5 * 5 = 100
Therefore, the station will first give away all three prizes to the 100th caller.
Now let's answer question 2.
The amount of money given away includes $15, $25, and the value of the concert ticket. The concert ticket is not given away alone, so its value needs to be added to the total amount.
Assuming the concert ticket has a value of T dollars, the total amount of money given away would be:
$15 + $25 + $T
Since the concert ticket is given away for free, we can assume its value to be $0. Therefore, the total amount of money given away would be:
$15 + $25 + $0 = $40
The number of tickets given away is 1, as the station gives away one concert ticket to the 100th caller.
15 = 3 * 5
25 = 5 * 5
100 = 5*5*2*2
so the least common multiple must have:
two 5s
two 2s
one 3
25 * 4 * 3 = 300
Back in your court :)