Harper surveyed 380 of the students in her school about their favorite color. 323 students said their favorite color was red. What percentage of the surveyed students said their favorite color was red?

85%

Step-by-step explanation:

Method 1: Set up a proportion

Set up an equation of the form:

part

whole

=

whole

part

=

percent

100

100

percent

Assign the variable

x

x to the unknown value:

x

=

x=

percent

percent

The question asks what

percent

percent of all the students is 323

Substitute the known values with the numbers given in the problem, and the unknown value with

x

x:

323

380

=

380

323

=

x

100

100

x

Solve for

x

x:

100

⋅

323

=

100⋅323=

380

⋅

x

380⋅x

Cross multiply

32300

380

=

380

32300

=

380

x

380

380

380x

Divide both sides by 20

85

%

=

85%=

x

x

Simplify

Method 2: Convert to decimal and multiply

Find

323

out of

380

as a decimal:

Find 323 out of 380 as a decimal:

323

380

=

380

323

=

0.85

0.85

Convert decimal to percent:

Convert decimal to percent:

0.85

×

100

=

0.85×100=

85

%

85%

Move decimal 2 places to the right

number

percent

323

85%

380

100%

step-by-step explanation: 4 cause 2+2=4