Question

Question #4772b

Answer 1

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.

Answer 2

`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`