One day, 32 of 80 people wore a red shirt to school. What percent of the 80 people did not wear a red shirt to school?

Question

Savannah Anderson · Accepted Answer

60 percent

To begin, let me count the number of people wearing different colored shirts: #=80-32 = 48# As a result, 48 of the 80 participants wore different colored shirts. This is in percentage terms: #=100times48/80 = 60# percent 60% is your response.

Genesis Allen · Answer

#60%#

A lot of detail given to help understanding. Normally a calculation of this type would only take a few lines.

A percentage is essentially just another type of fraction, but it differs from other fractions in that the denominator, or bottom number, is always 100. If the count of red shirts is 32 then the non red shirt count is #80-32 = 48# So this count as a fraction of the whole is #48/80# However, since the bottom number (denominator) must equal 100 in order for this to be a percentage, we write it as a "equivalent fraction." Let the unknown count be #x# giving: #color(green)(48/80-=x/100) # To find the value of the top number (numerator) of #x# we need to get it on its own. So we need to 'get rid' of the 100. We do this by changing it into 1 Multiply both sides by 100 times the color red. #color(green)(48/80-=x/100 color(white)("dddd")->color(white)("dddd") 48/80color(red)(xx100) color(white)("d") =color(white)("d") x/100color(red)(xx100) )# #color(green)(color(white)("ddddddddddd.d") ->color(white)("dddd") 48color(red)(xxcancel(100)^(10)/color(green)(cancel(80)^8)) color(white)("d") =color(white)("d") xcolor(red)(xxcancel(100)/color(green)(cancel(100))) )# #color(green)(color(white)("ddddddddddd.d") ->color(white)("ddddddd") cancel(48)^6xx10/cancel(8)^1 color(white)("d") =color(white)("d") x)# #color(green)(color(white)("ddddddddddd.d") ->color(white)("ddddddddddd") 60color(white)("dddd") =color(white)("d") x)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #x=60 ->x/100=60/100# #60/100# is the same thing as #60xx1/100# and #xx1/100# is the same thing as #%# So #60/100=60%#

Abigail Allen · Answer

undefined 68% of the 80 people did not wear a red shirt to school.