Question #4772b

2 Answers
Oct 4, 2016

Answer:

There were 200 questions on the quiz.

Explanation:

The part is obtained by multiplying the whole by the percent, written as a decimal, or
#p = rw#
In this case, 16 is the part answered correctly and the percent (generally referred to as a rate and thus represented by an r) is 0.08 when written as a decimal. So:
#16 = 0.08w#
#16/0.08 = w#
#200 = w#
Since the whole is 200, there were 200 questions on Jose language arts quiz.

Jul 10, 2017

Answer:

#x=200#

Explanation:

#color(blue)("Using the first principles method")#

Let the count of all questions be #x#

Correctly answered 8% of all questions #->8%xx x#

Count of his answers that were correct is 16

So we have #8%xx x = 16#

The % symbol is a bit like a unit of measurement but one that is worth #1/100#. So 8% #-> 8xx% ->8xx1/100=8/100#

So #8% xx x=16# becomes

#8/100 x =16#

Multiply both sides by #color(red)(100/8)# this changes #8/100# into 1

#color(green)(8/100color(red)(xx100/8)xx x" "=" "16color(red)(xx100/8))#

#" "color(green)(8/(color(red)(8))xx(color(red)(100))/100 xx x" "=" "16/(color(red)(8))xxcolor(red)(100))#

#1xx1xx x=2xx100#

#x=200#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Using the short cut method")#

When you move a multiply to the other side of the equals sign you change it to divide. To divide by a fraction you 'turn it upside down' (invert) and then multiply.

#8/100 x =16#

#x=16xx100/8#

#x=2xx100#

#x=200#