Question

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?

⇓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

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