**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

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

Post a Comment