The maximum number of guests Alex can invite is 16 where each guest will get 6 bags of drinks and 5 bags of Takis without wasting any of the bags.
Given: Alex has 96 drinks and 80 bags of Takis. To find what is the maximum number of guests he can invite.
What is GCD?
GCD is the greatest common divisor. The GCD for a given set of numbers can be defined as the greatest number which can divide all the numbers from the given set of numbers. If x and y are two numbers, the GCD of these two numbers can be represented as gcd(x, y). It is also known as the highest common divisor (HCF).
How to calculate the GCD of given two numbers x and y?
To calculate the GCD of the given two numbers x and y, first, we need to find all the factors of these two given numbers.
Let's say the factors of x be 1, x₁, x₂, x₃, m, .... and x (every number divides itself, so every number is a factor of itself)
and the factors of y be 1, y₁, y₂, y₃, m .... and y (every number divides itself, so every number is a factor of itself)
Therefore,
x = 1, x₁, x₂, x₃, m, .... and x
y = 1, y₁, y₂, y₃, m .... and y
We can see that out of all the factors of x and y, the greatest number that is a common factor for both x and y is m.
So, gcd(x, y) = m
Let's solve the given problem.
Alex has 96 bags of drinks and 80 bags of Takis.
First we need to find the factors of 96 and 80 respectively.
80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Now we have to find the gcd of 80 and 96.
Therefore, from the above factors of 80 and 96, we see that 16 is the greatest common factor.
So, gcd(80, 96) = 16
The max number of guests Alex can invite is 16.
Drinks for each guest = 96 / 16 = 6
Takis for each guest = 80 / 16 = 5
Hence the maximum number of guests Alex can invite is 16 where each guest will get 6 bags of drinks and 5 bags of Takis without wasting any of the bags.
Know more about "greatest common divisor (GCD)" here: brainly.com/question/2263855
#SPJ9
