The ratio of the number of adults to the number of students at the prom is 1:10. Last year there were 477 more students than adults at the prom. The school is expecting the same attendance this year, how many adults have to attend the prom?
To find the number of adults who have to attend the prom, we need to determine the number of students first. Let's start by setting up some equations based on the given information:
Let's assume the number of adults at the prom is "A" and the number of students is "S."
According to the given ratio, the number of adults to students is 1:10. This can be written as:
A/S = 1/10
Last year, there were 477 more students than adults at the prom. So we can set up another equation:
S - A = 477
Now, we have a system of two equations with two variables:
A/S = 1/10 ---(1)
S - A = 477 ---(2)
To solve this system, we can use substitution or elimination method. In this case, let's use the substitution method to find the value of S and A.
From equation (1), we can rewrite A/S as A = (1/10)S.
Now, substitute this value of A into equation (2):
S - (1/10)S = 477
Combining like terms, we get:
(9/10)S = 477
To isolate S, divide both sides of the equation by (9/10):
S = 477 * (10/9)
S = 530
So, the number of students expected to attend the prom this year is 530.
Now, we can substitute this value of S into equation (1) to find A:
A/S = 1/10
A/530 = 1/10
Cross-multiply:
A = (1/10) * 530
A = 53
Therefore, the number of adults that have to attend the prom is 53.
10 a = s
a + 477 = s
477 = 9 a