# 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?

Jul 29, 2018

9 bracelets

#### Explanation:

the number of bracelets Sarah wants to make = x

converting the sentence into an equation:

21 = 70% xx x

$21 = \frac{70}{100} \times x$

$x = 21 \times \frac{100}{70} = 30$

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.

Jul 29, 2018

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")

$x = \frac{21 \times 30}{70}$

$x = 9$

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

Jul 29, 2018

Need to make 9 more

Detailed explanation given

#### Explanation:

$\textcolor{b l u e}{\text{This is how to think about what percentage is}}$

The symbol % is a bit like a unit of measurement but one that is worth: $\frac{1}{100}$ of something.

So we have:

$70 \textcolor{w h i t e}{\text{dd")ubrace("of")color(white)("dd") ubrace(1/100" of something}}$
$\textcolor{w h i t e}{\text{dddd")darrcolor(white)("ddddddddd}} \downarrow$

ubrace(70color(white)("dd")xxcolor(white)("ddddddddd")%)
$\textcolor{w h i t e}{\text{ddddddd.}} \downarrow$
color(white)("ddddddd")70%color(white)("d")->color(white)("dd")70/100" of something"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

Let the unknown total count of bracelets be $b$

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

$\textcolor{w h i t e}{\text{d}} \frac{70}{100} \times b = 21$

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 $\frac{70}{100}$ on the left. We do this by turning it into the value of 1

Multiply both sides by $\textcolor{red}{\frac{100}{70}}$

$\textcolor{g r e e n}{\frac{70}{100} \times b \textcolor{w h i t e}{\text{d")=color(white)("d") 21 color(white)("dddd")->color(white)("dddd")70/100color(red)(xx100/70)xx bcolor(white)("d}} = 21 \textcolor{red}{\times \frac{100}{70}}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddddddddd")->color(white)("ddddd") 70/color(red)(70)xxcolor(red)(100)/100xxbcolor(white)("d}} = 30}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddddddddd")-> color(white)("dddddd")ubrace(1color(white)("d")xxcolor(white)("d")1)color(white)("d}} \times b = 30}$

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

$\textcolor{g r e e n}{b = 30}$

So the total count of beads is $30$
Already made 21 $\to \textcolor{w h i t e}{\text{dddd.d")ul(21larr" Subtract}}$
color(white)("dddddddddddddddddddddd")9larr" Yet to be made"