Esther, Ivory, Cindy and Hazel went to buy a souvenir for their father. They shared the cost equally among themselves. However, Hazel forgot to bring her money. So, the other 3 girls paid for the souvenir first. Cindy paid
35 of the amount Esther and Ivory paid. Ivory paid $3 more than Esther. The next day, Hazel returned $7 to Cindy and some money to Esther and Ivory. How much did Hazel return to
- Esther?
- Ivory?
|
Esther |
Ivory |
Cindy |
Hazel |
Total |
Comparing the amounts 3 girls paid first |
5 u
|
3 u
|
|
8 u
|
Comparing the amounts 2 girls paid first |
1 p
|
1 p + 3
|
|
|
|
Amounts that each girl paid for Hazel first |
- ? |
- ? |
- 7
|
+ 7 + ? |
|
Comparing the amounts each girl should pay |
1x2 = 2 u |
1x2 = 2 u |
1x2 = 2 u |
1x2 = 2 u |
4x2 = 8 u |
(a)
The total amount that the 4 girls paid is repeated. Make the total amount the same. LCM of 4 and 8 is 8.
Extra amount that Cindy paid
= 3 u - 2 u
= 1 u
1 u = 7
Total amount that Esther and Ivory paid at first
= 5 u
= 5 x 7
= $35
1 p + 1 p + 3 = 35
2 p = 35 - 3
2 p = 32
1 p = 32 ÷ 2 = 16
Amount that Hazel needed to pay Esther
= 1 p - 2 u
= 16 - 2 x 7
= 16 - 14
= $2
(b)
Amount that Hazel needed to pay Ivory
= (1 p + 3) - 2 u
= (16 + 3) - 2 x 7
= 19 - 14
= $5
Answer(s): (a) $2; (b) $5