## Question

primary 5 | Maths | Percentage

Anyone can contribute an answer, even non-tutors.

##### Joel

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Kindly help

Date Posted: 1 year ago
Views: 118
J
1 year ago
10% fewer blue dresses were sold on Tuesday than on Monday, but 10% more red dresses were sold on Tuesday than Monday.

So the additional number of red dresses sold on Tuesday could cover the decrease in blue dresses sold on Tuesday, and still result in an overall increase of 5% of all dresses sold as compared to Monday.

This tells us that :

10% of red dresses sold on Monday = 10% of blue dresses sold on Monday + 5% of all dresses sold on Monday.

Multiply by 10 ,

100% of red dresses sold on Monday
= 100% of blue dresses sold on Monday
+ 50% of all dresses sold on Monday.

This is the same as saying :

Red dresses sold on Monday = blue dresses sold on Monday + ½ blue dresses + ½ red dresses sold on Monday

(50% of all dresses sold on Monday = 50% of blue dresses sold on Monday + 50% of red dresses sold on Monda

Let R represent total number of red dress sold on Monday and B represent total number of blue dresses sold on Monday.

From our earlier equation,

R = B + ½R + ½B
Multiply both sides of equation by 2,

2R = 2B + R + B
R = 3B

So ratio of red to blue sold on Monday is 3 : 1, since 1 unit of red equals 3 units of blue. Total is 4 units.

Percentage sold on Monday that were red
= 3/4 x 100%
= 75%
J
1 year ago
Alternatively, let number of red dresses sold on Monday be 10R, and number of blue dressses sold on Monday be 10B.
Total = 10A + 10B

On Tuesday,

Red dresses sold = 11R
Blue dresses sold = 9B
Total = 11R + 9B

Total sold on Tuesday is 5% more than Monday.

5% of Monday total = 5% of red on Monday + 5% of blue on Monday

5% of red on Monday is ½R
5% of blue on Monday is ½B

So 11R + 9B = 10R + 10B + ½R + ½B

11R + 9B = 10½R + 10½B
½R = 1½B
R = 3B

Ratio of red to blue is 3 : 1 , since 1 unit of red is equal to 3 times 1 unit of blue.

Total = 4 units

Percentage = 3/4 x 100% = 75%

clear {{ downvoteCount * -1 }} Downvotes
1st
Guess and Check Method:
There should be more red dresses sold than blue dresses because overall, there was an increase in number of dresses sold on Tue compared to Mon.

Hope the solution helps.
Date Posted: 1 year ago
Joel
1 year ago
Thanks for the help
J
1 year ago
The problem with guess and check here is that as the are numbers of any dresses are given, there are many solutions. So to say that the number of dresses is a certain number would technically be incorrect.

To guess and check , the student may not know where to start and it can take a very long time to figure out the correct percentages.

Joel, refer to my solutions in the comment section for a general solution to the question which does not involve any numbers of dresses