The results of a survey are shown. In the survey, 28 students said their favorite dessert is ice cream. A) how many students were surveyed? B) how many students said their favorite dessert is pie? _____________________Thanks!

A) We can write this problem as:

35% of what number is 28?

"Percent" or "%" means "out of 100" or "per 100", Therefore 35% can be written as #35/100#.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number of students we are looking for "s".

Putting this altogether we can write this equation and solve for #s# while keeping the equation balanced:

#35/100 xx s = 28#

#color(red)(100)/color(blue)(35) xx 35/100 xx s = color(red)(100)/color(blue)(35) xx 28#

#cancel(color(red)(100))/cancel(color(blue)(35)) xx color(blue)(cancel(color(black)(35)))/color(red)(cancel(color(black)(100))) xx s = 2800/color(blue)(35)#

#s = 80#

80 students were surveyed.

B) Now that we know how many students were surveyed we can rewrite this problem as:

15% of 80 is what?

Again, "Percent" or "%" means "out of 100" or "per 100", Therefore 15% can be written as #15/100#.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number of students who like pie: "p".

Putting this altogether we can write this equation and solve for #p# while keeping the equation balanced:

#p = 15/100 xx 80#

#p = 1200/100#

#p = 12#

12 Students have pie as their favorite desert