Mrs Chen bought some eggs. She used 1/2 of them to make tarts and 1/4 of the remainder to make a cake. She had 9 eggs left. How many eggs did she buy?

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Answer 1 · 2016-09-24T17:51:31

She starts with 24 eggs.

We can work through this question, by using only fractions.

Mrs Chen used $1/2$ of the eggs.

This means she has $1/2$ of the eggs left.

She uses another $1/4$ of the $1/2$ that are left.
$1/4 xx 1/2 = 1/8$

Together she has used:

$1/2+1/8$

$= 4/8 +1/8 = 5/8$

If $5/8$ have been used, it means that $8/8-5/8 = 3/8$ is left.

$3/8$ of the total number of eggs is $9$ eggs

$1/8$ of the total is $9 div 3 = 3$ eggs

$8/8$ is the total number of eggs. $3xx 8 = 24$ eggs

Check:
$1/2 xx 24 = 12$ eggs used. 12 eggs are left

$1/4 xx 12 = 3$ more eggs are used.

$12-3 = 9$ eggs are left from the 24.

Answer 2 · 2016-10-03T19:07:09

I have chosen to write this in a similar way to that used by algebra as an introduction to the methods.

$"total count" = 24" eggs"$

First use $->1/2$
Second use $->1/4 " remainder "->1/4xx1/2=1/8$

Total use is:

$color(blue)(1/2+1/8)color(red)(" " ->" " [1/2xx4/4]+1/8)color(green)(" " =" " 4/8+1/8)color(purple)(" "=" "5/8)$

Therefor not used is: $" "1-5/8 = 3/8" total count"$

But not used is 9 eggs

$=>color(brown)( 3/8" total count "=" "9" eggs")$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
But we need 1 of total count. Not $3/8$ of it. Thus we need to change the $3/8$ into 1

Multiply both sides by $color(blue)(8/3)$
Note that this is where the shortcut method of cross multiply comes from.

$color(brown)(color(blue)(8/3xx)[3/8xx" total count"] = color(blue)(8/3xx)[9" eggs"])$

$3/3xx8/8xx"total count"=(8xx9)/3" eggs"$

$" "1xx1xx"total count"=(72)/3" eggs"$

Note that $1xx"total count is the same as total count"$

$color(white)()$

$" "color(purple)(bar(ul(|color(white)(2/2)"total count" = 24" eggs"color(white)(2/2)|)))$