Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.
Solution
(Note: The working has been amended (in blue) on 17 Sep 08 to make the working clearer.)
Cost of 1 dictionary ----- 1 unit + $4
Cost of 1 comic ----- 1 unit
Comics ----- 120%
Dictionary ----- 100%
Total 220% ----- $1496
10% ----- $1496 divided by 22 = $68
(Dictionaries) 100% ----- $680
Cost of 1 comic ----- 1 unit
Comics ----- 120%
Dictionary ----- 100%
Total 220% ----- $1496
10% ----- $1496 divided by 22 = $68
(Dictionaries) 100% ----- $680
Comics ----- $1496 - $680 = $816
But we know that the ratio
comics : dictionaries
3 : 2
Comics
3 units ----- $816
1 unit ----- $272
Dictionaries
2 units + ? groups of $4 ------ $680
(2 x $272) + ? grps of $4 ----- $680
? grps of $4 ----- $680 - $544 = $136
? grps ----- $136 divided by 4 = 34 groups of $4
[Every $4 difference ---- 1 dictionary was bought
$136 difference ----- $136 divided by $4 = 34 (dictionaries)]
Dictionaries ----- $680
$680 divided by 34 dictionaries = $20 per dictionary
Answer: One dictionary cost $20.
Dictionaries ----- $680
$680 divided by 34 dictionaries = $20 per dictionary
Answer: One dictionary cost $20.
4 comments:
Dear Mr Song
The total cost of the comics was 20% more than the total cost of the dictionaries.
Difference between what was paid for dictionaries and comics,
120% - 100% = 20%
20% ----- $68 x 2 = $136
Every $4 difference ---- 1 dictionary was bought
$136 difference ----- $136 divided by $4 = 34
Why is 20%(136) equated to the value of the additional $4 for dictionary?
I have added more steps in the main post to make the working clearer.
Hope that helps.
thanks for the answers.
there is just one thing I don't understand.....
? grps of $4 ----- $680 - $544 = $136
? grps ----- $136 divided by 4 = 34 groups of $4
where did $544 came from?
thanks
544 is from the 2 units.
1 unit is 272.
2 units ----- 2 x 272 = 544
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