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Please assist. Thank you.

11. Dave had some 50-cent coins. Wayne had some $1 coins. Dave gave 50% of his coins to Wayne and Wayne gave 50% of his coins to Dave. Wayne used some of the 50-cent coins to buy a book that cost $5. Dave used some of his $1 coins to buy a bag that cost $16. After that the ratio of the number of 50-cent coins to $1 coin Dave had was 1 : 2 and the number of 50-cent coins to the number of $1 coins Wayne had was 1 : 5.
How much did Dave have at first?

Answer

⇓After giving each other half of their coins, both Dave and Wayne has the same number of 50c and $1 coins to start off.

Dave

50c $1  
 ⇓ -16 ⇓ $16 for the bag
1u 2u  

Wayne

50c $1  
-10 ⇓  ⇓ $5=> 10 pieces of 50c coins
1p 5p  

number of 50c coins , 1u = 1p + 10 –(1)
number of $1 coins, 5p = 2u + 16 -(2)

(1) X 2
2u = 2p + 20
2p = 2u – 20 —(3)

(2) – (3)
3p = 36
p = 12

1u = 1p + 10 = 22

Before they bought their stuff, the number of coins is
50c coins = 1u = 22 coins
$1 coins = 5p = 60 coins.

Before Dave gave half of his 50c coins to Wayne. the numbe of 50c he has = 22 X 2 = 44 coins.
Amount he has = 44 X 0.5 = $22 ###

0 Replies 3 Likes ✔Accepted Answer

Hi,

This is a typical Matrix question with 2 persons and 2 items.

First, Dave gave half of his money to Wayne, and then Wayne spent 10 coins. (10 x 0.5 = 5)
So Dave has 2 units.

      50 cent        $1             Total        
Dave     1u    
Wayne        1u – 10    

Next, Dave has 50-cent and $1 in the ratio of 1 : 2, after he has used 16 coins. ($1 x 16 = 16)
So Wayne must have given him 2u + 16 coins.

      50 cent        $1             Total        
Dave     1u 2u 3u
Wayne        1u – 10 2u + 16 3u + 6 

Lastly Wayne’s 50-cent to $1 is 1 : 5.

(1u – 10) / 1   =   (2u + 16) / 5
5u – 50 = 2u + 16                 (Cross Multiplication)
5u – 2u = 16 + 50
3u = 66
1u = 66 / 3 = 22
2u = 22 x 2 = 44 coins

44 x 0.5 = $22

Some other problems of the same category are:

  1. Boys and Girls of 2 classes
  2. Swimmer and Non-swimmer for Boys and Girls
  3. Wear or not wear spectacles for Boys and Girls
  4. Men and Women as adult and Boys and Girls as children

 

1 Reply 3 Likes

Thank you very much for your input, Khong Pek Mao.

0 Replies 1 Like
Dave Wayne
50c -> 1u 50c -> 1u
$1 -> 1p $1 -> 1p

Wayne spent $5 of 50 cents coin -> 10 coins

Dave spent $16 of $1 coin -> 16 coins

Dave Wayne
50c -> 1u 50c -> 1u – 10
$1 -> 1p – 16 $1 -> 1p

Dave’s coins -> 1 : 2

2 x (1u) = 1p – 16

1p = 2u + 16

Wayne’s coins -> 1 : 5

5 x (1u – 10) = 1p

1p = 5u – 50

5u – 50 = 2u + 16

3u = 66

1u = 22

In the beginning, Dave had 2u = 2 x 22 = 44  50 cents coin

He had 44 x $0.50 = $22 at first

1 Reply 4 Likes

That’s fast!
Thank you very much, Ender & BigDevil.

0 Replies 0 Likes