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?

2 Answers
Sep 24, 2016

She starts with 24 eggs.

Explanation:

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.

Oct 3, 2016

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"#

Explanation:

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)|)))#