Question #4772b

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Question #4772b

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Answer 1 · 2016-10-04T22:44:55

There were 200 questions on the quiz.

Explanation:

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

Answer 2 · 2017-07-10T10:10:09

$x = 200$ $x=200$

Explanation:

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

Let the count of all questions be $x$ $x$

Correctly answered 8% of all questions $\to 8 % \times x$ $->8%xx x$

Count of his answers that were correct is 16

So we have $8 % \times x = 16$ $8%xx x = 16$

The % symbol is a bit like a unit of measurement but one that is worth $\frac{1}{100}$ $1/100$ . So 8% $\to 8 \times % \to 8 \times \frac{1}{100} = \frac{8}{100}$ $-> 8xx% ->8xx1/100=8/100$

So $8 % \times x = 16$ $8% xx x=16$ becomes

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

Multiply both sides by $\frac{100}{8}$ $color(red)(100/8)$ this changes $\frac{8}{100}$ $8/100$ into 1

$\frac{8}{100} \times \frac{100}{8} \times x = 16 \times \frac{100}{8}$ $color(green)(8/100color(red)(xx100/8)xx x" "=" "16color(red)(xx100/8))$

$\frac{8}{8} \times \frac{100}{100} \times x = \frac{16}{8} \times 100$ $" "color(green)(8/(color(red)(8))xx(color(red)(100))/100 xx x" "=" "16/(color(red)(8))xxcolor(red)(100))$

$1 \times 1 \times x = 2 \times 100$ $1xx1xx x=2xx100$

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

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.

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

$x = 16 \times \frac{100}{8}$ $x=16xx100/8$

$x = 2 \times 100$ $x=2xx100$

$x = 200$ $x=200$

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Question #4772b

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