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?

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.

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#

#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"#