In a recent survey, 248 students or 32% of the sample said they worked part time during the summer. How many students were surveyed?

Question

Isaiah Anthony · Accepted Answer

There were 775 student surveyed.

This question can be rewritten as: 248 is 32% of what? "Percent" or "%" means "out of 100" or "per 100", Therefore 32% can be written as #32/100#. When dealing with percents the word "of" means "times" or "to multiply". Finally, lets call the number we are looking for "n". Putting this altogether we can write this equation and solve for #n# while keeping the equation balanced: #248 = 32/100 xx n# #100/32 xx 248 = 100/32 xx 32/100 xx n# #24800/32 = cancel(100)/cancel(32) xx cancel(32)/cancel(100) xx n# #775 = n#

Ethan Adkins · Answer

undefined To find the total number of students surveyed, you can use the equation:
$$ \text{Total number of students surveyed} = \frac{\text{Number of students who worked part time during the summer}}{\text{Percentage of students who worked part time during the summer}} \times 100 $$
Plugging in the values:
$$ \text{Total number of students surveyed} = \frac{248}{32\%} \times 100 $$
$$ \text{Total number of students surveyed} = \frac{248}{0.32} \times 100 $$
$$ \text{Total number of students surveyed} = 775 $$
So, 775 students were surveyed.