This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Sunday, August 31, 2008

Pei Chun Public Sch 2007 PSLE Math Prelim Q48

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

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

keentolearn said...

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?

Excel Eduservice said...

I have added more steps in the main post to make the working clearer.

Hope that helps.

Anonymous said...

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

Excel Eduservice said...

544 is from the 2 units.
1 unit is 272.
2 units ----- 2 x 272 = 544