# Question 4772b

Oct 4, 2016

There were 200 questions on the quiz.

#### Explanation:

The part is obtained by multiplying the whole by the percent, written as a decimal, or
$p = r w$
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:
$16 = 0.08 w$
$\frac{16}{0.08} = w$
$200 = w$
Since the whole is 200, there were 200 questions on Jose language arts quiz.

Jul 10, 2017

$x = 200$

#### Explanation:

$\textcolor{b l u e}{\text{Using the first principles method}}$

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 $\frac{1}{100}$. So 8% -> 8xx% ->8xx1/100=8/100

So 8% xx x=16 becomes

$\frac{8}{100} x = 16$

Multiply both sides by $\textcolor{red}{\frac{100}{8}}$ this changes $\frac{8}{100}$ into 1

$\textcolor{g r e e n}{\frac{8}{100} \textcolor{red}{\times \frac{100}{8}} \times x \text{ "=" } 16 \textcolor{red}{\times \frac{100}{8}}}$

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

$1 \times 1 \times x = 2 \times 100$

$x = 200$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Using the short cut method}}$

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.

$\frac{8}{100} x = 16$

$x = 16 \times \frac{100}{8}$

$x = 2 \times 100$

$x = 200$