the ratio of the number of adults to the number of students at the prom has to be 1:10 last year there were 477 more students than adults at the prom if the school is expecting the same attendance this year how many adults attended the prom
number of adults --- x
number of students --- 10x , (note that x : 10x = 1 : 10)
10x - x = 477
9x = 477
x = 53
so 53 adults attended and 530 students
check: is 530-53 = 477 ? sure is!
Well, at least we know the prom wasn't a party for clowns only! Let's do some math to find out the number of adults who attended last year.
If the ratio of adults to students at the prom is 1:10, it means that for every adult, there are 10 students.
Let's assume the number of adults is represented by "x". In that case, the number of students would be 10x (since there are 10 students for every adult).
Last year, there were 477 more students than adults, so we can set up an equation:
10x - x = 477
Simplifying this equation gives us:
9x = 477
Dividing both sides by 9:
x = 53
So, the number of adults who attended the prom last year was 53.
Since the school is expecting the same attendance this year, we can assume that 53 adults will attend this year's prom as well.
Let's solve this step-by-step:
Step 1: Set up the equation
Let's denote the number of adults as "A" and the number of students as "S." According to the given information, the ratio of adults to students is 1:10. Therefore, we can write the equation as:
A / S = 1 / 10
Step 2: Formulate another equation
We are also given that last year, there were 477 more students than adults at the prom. We can express this as:
S = A + 477
Step 3: Simplify the equations
Since we have two variables, we need to substitute the value of "S" from the second equation into the first equation. Thus, our new equation becomes:
A / (A + 477) = 1 / 10
Step 4: Cross-multiply and solve the equation
Cross-multiplying gives us:
10A = A + 477
Simplifying further, we have:
10A - A = 477
9A = 477
Finally, dividing both sides by 9, we find:
A = 477 / 9
A ≈ 53
Therefore, approximately 53 adults attended the prom.
To find the number of adults attending the prom, we need to set up an equation based on the given information.
Let's assume that the number of adults last year was A, and the number of students was S.
According to the ratio, the number of adults to the number of students is 1:10. This can be written as:
A/S = 1/10
We also know that last year there were 477 more students than adults:
S - A = 477
Now, we can solve this system of equations to find the values of A and S. Let's start by solving for A:
From the first equation, we can rewrite it as A = (1/10)S.
Substituting this into the second equation, we get:
S - (1/10)S = 477
Simplifying, we have:
(9/10)S = 477
Multiply both sides by (10/9) to get:
S = (477 * 10) / 9
S = 530
So, there were 530 students attending the prom last year.
To find the number of adults, substitute this value back into the first equation:
A = (1/10) * 530
A = 53
Therefore, there were 53 adults attending the prom last year.
Since the school is expecting the same attendance this year, the number of adults attending the prom this year would also be 53.