Rachel, Shiyun, Tammy and Yen went to buy a gift for their father. They shared the cost equally among themselves. However, Yen forgot to bring her money. So, the other 3 girls paid for the gift first. Tammy paid
79 of the amount Rachel and Shiyun paid. Shiyun paid $4 more than Rachel. The next day, Yen returned $18 to Tammy and some money to Rachel and Shiyun. How much did Yen return to
- Rachel?
- Shiyun?
|
Rachel |
Shiyun |
Tammy |
Yen |
Total |
Comparing the amounts 3 girls paid first |
9 u
|
7 u
|
|
16 u
|
Comparing the amounts 2 girls paid first |
1 p
|
1 p + 4
|
|
|
|
Amounts that each girl paid for Yen first |
- ? |
- ? |
- 18
|
+ 18 + ? |
|
Comparing the amounts each girl should pay |
1x4 = 4 u |
1x4 = 4 u |
1x4 = 4 u |
1x4 = 4 u |
4x4 = 16 u |
(a)
The total amount that the 4 girls paid is repeated. Make the total amount the same. LCM of 4 and 16 is 16.
Extra amount that Tammy paid
= 7 u - 4 u
= 3 u
3 u = 18
1 u = 18 ÷ 3 = 6
Total amount that Rachel and Shiyun paid at first
= 9 u
= 9 x 6
= $54
1 p + 1 p + 4 = 54
2 p = 54 - 4
2 p = 50
1 p = 50 ÷ 2 = 25
Amount that Yen needed to pay Rachel
= 1 p - 4 u
= 25 - 4 x 6
= 25 - 24
= $1
(b)
Amount that Yen needed to pay Shiyun
= (1 p + 4) - 4 u
= (25 + 4) - 4 x 6
= 29 - 24
= $5
Answer(s): (a) $1; (b) $5