Question

Sarah has made 21 bracelets to sell at craft fair. If this is 70% of the bracelets she wants to make, how many more bracelets does she need to make?

Answer 1

9 bracelets

Explanation:

the number of bracelets Sarah wants to make = x

converting the sentence into an equation:

`21 = 70% xx x`

`21 = 70/100 xx x`

`x = 21 xx 100/70=30`

Sarah wants to make 30 bracelets, and she has made 21 so far. That means, she'll need to make = 30 - 21 = 9 more bracelets.

Answer 2

She will need to make `9` more bracelets which will give a total of `30`

Explanation:

Questions involving percentages can always be answered using direct proportion.

Compare the percentages with the numbers.

`21` bracelets represents `70%`

The total amount she wishes to make represents `100%`, so she has another `30%` to make:

`x/30 =21/70" "(larr "bracelets")/(larr "percent")`

`x = (21xx30)/70`

`x = 9`

She will need to make `9` more bracelets which will give a total of `30`

Answer 3

Need to make 9 more

Detailed explanation given

Explanation:

`color(blue)("This is how to think about what percentage is")`

The symbol % is a bit like a unit of measurement but one that is worth: `1/100` of something.

So we have:

`70color(white)("dd")ubrace("of")color(white)("dd") ubrace(1/100" of something")`
`color(white)("dddd")darrcolor(white)("ddddddddd")darr`

`ubrace(70color(white)("dd")xxcolor(white)("ddddddddd")%)`
`color(white)("ddddddd.")darr`
`color(white)("ddddddd")70%color(white)("d")->color(white)("dd")70/100" of something"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Let the unknown total count of bracelets be `b`

Then we have: `70%" of "b=21`

`color(white)("d")70/100xx b =21`

We need to end up with just a `b` on one side of the equals and everything else on the other side. So we need to 'get rid' of the `70/100` on the left. We do this by turning it into the value of 1

Multiply both sides by `color(red)(100/70)`

`color(green)(70/100xxb color(white)("d")=color(white)("d") 21 color(white)("dddd")->color(white)("dddd")70/100color(red)(xx100/70)xx bcolor(white)("d") =21 color(red)(xx 100/70))`

`color(green)(color(white)("ddddddddddddddddd")->color(white)("ddddd") 70/color(red)(70)xxcolor(red)(100)/100xxbcolor(white)("d")= 30 )`

`color(green)(color(white)("ddddddddddddddddd")-> color(white)("dddddd")ubrace(1color(white)("d")xxcolor(white)("d")1)color(white)("d")xxb =30)`

`color(white)("d")color(green)( color(white)("dddddddddddddddd")->color(white)("ddddddddd")1 color(white)("ddd")xx b=30)`

`color(green)(b=30)`

So the total count of beads is `30`
Already made 21 `->color(white)("dddd.d")ul(21larr" Subtract")`
`color(white)("dddddddddddddddddddddd")9larr" Yet to be made"`