Ratio of adults to students is 1: 10. last yr there 477 more students than adults at prom. if school is expecting the same attendance this year, how many adults have to attend?

X -number of adults
x+477 -number of students

We want to make students 10 times more numerous then adults. When creating equation we need to multiply number of adults by 10, to make both sides even (thats why there is 10x, so ten times the number of students)
x+477=10x      /-x from both sides
477=9x
53=x

Let's check
is 53 ten times less then 53+477(530). It is.
So 53 adults have to attend the prom.