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Question

Hi,

 

I get this question from the assessment book. 

In a sale, Nancy spent $2960 on some blouses and skirts. Each blouse cost $32 and each skirt cost 25% as much as each blouse. She bought 20 more skirts than blouses. How many skirts did she buy?

Ans : 25% x $32 = $8

$32 + $8 + $40

20 x $8 = $160

($2960 – $160) ÷ 40 = 70

70 + 20 = 90

 

I cannot understand why the last part is divided by 40. Isn’t it blouses and skirts share the unit ?

My understanding is as follow:

($2960 – $160)= $2800

$2800 ÷ 2 = $1400

$1400 + $160 = $1560

$1560 ÷ 40 = 39

39 + 20 = 59

Answer

Hi Musicstar. I believe your confusion Is the cost of each skirt. The skirt does not cost 125%. It costs 25% of blouse and so it is only $8 each. $40 is 1 set of 1 blouse and 1 shirt. 

Taking away the cost of excess 20 skirts ($160), the remainder $2800 is 70 sets of 1 blouse and 1 shirt ($40 per set)

So there are 90 skirts (70+20). 


Oh. Maybe your confusion is not that, could be you think the balance cost $2800 is shared equally between equal no. of blouses and skirts. 

If so this is a misconception. Think about those coins type questions.  

5pcs of $1-coins and 5pcs of 20c-coins in the piggy bank (total $6) doesn’t mean $3 of $1-coins and $3 of 20c-coins.

solution should be: total value/value per set = no. of sets

misconception: half total value / value per pc = no. of pcs  


If your algebra is good, you can deduce the same thing from Khong’s workings / Ender’s picture. 

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post-20185

My understanding is as follow:

($2960 – $160)= $2800

From here onwwards is wrong.

$2800 ÷ 2 = $1400          X
$1400 + $160 = $1560    X
$1560 ÷ 40 = 39                X
39 + 20 = 59                       X

When you minus $160 and left $2800, it does not mean the cost of the skirt is half of it. It just means for the same number of skirts and blouses, they cost $2800 together.

Refer to my picture for understanding how the $2800 is breakdown. You will realized that the skirt do not cost half of $2800 as what you have initially thought.

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This is a Quantity Amount question. 

  Blouse    skirt     Total      
 Quantity   1u  1u + 20        
 Each   32    
Product  32u 8u + 160 40u + 160   

40u + 160 = 2960

40u = 2960 – 160

40u = 2800

1u = 70

70 + 20 = 90

 

0 Replies 0 Likes

This is a Quantity Amount question. 

  Blouse    skirt     Total      
 Quantity   1u  1u + 20        
 Each   32    
Product  32u 8u + 160 40u + 160   

40u + 160 = 2960

40u = 2960 – 160

40u = 2800

1u = 70

70 + 20 = 90

 

0 Replies 1 Like