Erika, Rachel, Lucy and Diana went to buy a gift for their grandfather. They shared the cost equally among themselves. However, Diana forgot to bring her money. So, the other 3 girls paid for the gift first. Lucy paid
79 of the amount Erika and Rachel paid. Rachel paid $4 more than Erika. The next day, Diana returned $18 to Lucy and some money to Erika and Rachel. How much did Diana return to
- Erika?
- Rachel?
|
Erika |
Rachel |
Lucy |
Diana |
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 Diana 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 Lucy paid
= 7 u - 4 u
= 3 u
3 u = 18
1 u = 18 ÷ 3 = 6
Total amount that Erika and Rachel 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 Diana needed to pay Erika
= 1 p - 4 u
= 25 - 4 x 6
= 25 - 24
= $1
(b)
Amount that Diana needed to pay Rachel
= (1 p + 4) - 4 u
= (25 + 4) - 4 x 6
= 29 - 24
= $5
Answer(s): (a) $1; (b) $5