Use the list found in Part A for the people that will receive a plasma ball.
A
Guest 350
B
7 people
Practice makes perfect
A science museum is giving away a magnetic liquid kit to every 50th guest and a plasma ball to every 35th guest until someone receives both prices. Let's make two lists that represent the guests who will win each prize.
Winners of kit &= 35,70,105,140,175,210,...
Winners of ball &= 50,100,150,200,250,300,...
To find which numbered guest will receive both a magnetic liquid kit and a plasma ball, we can find the least common multiple (LCM) of 50 and 35. Recall that the LCM of two numbers is the smallest whole number that is a multiple of both numbers. To find the LCM, we can follow two steps.
Express each number as a product of its prime factors.
Let's start by finding the prime factors with the factor tree of each number.
The red circles are the prime factors of the given numbers. We can use these factors to write the prime factorization of each number.
35 &= 5 * 7
50 &= 2 * 5 * 5 = 2* 5^2
Now let's identify the highest power of each prime factor.
35 &= 5* 7
50 &= 2 * 5^2
Finally, we multiply these powers together to find the LCM of 35 and 50.
To find the number of people that will receive a plasma ball, we can recall the list that represents the numbered guests who will win a plasma ball.
Winners of ball= 50,100,150,200,250,300,350
Since the museum is giving away prizes until guest 350, every guest with a number equal to or less than 350 will receive a plasma ball.
50,100,150,200,250,300,350
Only 7 people will receive a plasma ball.
