Marion, Xandra, Yen and Winnie went to buy a gift for their cousin. They shared the cost equally among themselves. However, Winnie forgot to bring her money. So, the other 3 girls paid for the gift first. Yen paid
79 of the amount Marion and Xandra paid. Xandra paid $4 more than Marion. The next day, Winnie returned $30 to Yen and some money to Marion and Xandra. How much did Winnie return to
- Marion?
- Xandra?
|
Marion |
Xandra |
Yen |
Winnie |
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 Winnie first |
- ? |
- ? |
- 30
|
+ 30 + ? |
|
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 Yen paid
= 7 u - 4 u
= 3 u
3 u = 30
1 u = 30 ÷ 3 = 10
Total amount that Marion and Xandra paid at first
= 9 u
= 9 x 10
= $90
1 p + 1 p + 4 = 90
2 p = 90 - 4
2 p = 86
1 p = 86 ÷ 2 = 43
Amount that Winnie needed to pay Marion
= 1 p - 4 u
= 43 - 4 x 10
= 43 - 40
= $3
(b)
Amount that Winnie needed to pay Xandra
= (1 p + 4) - 4 u
= (43 + 4) - 4 x 10
= 47 - 40
= $7
Answer(s): (a) $3; (b) $7