Fiona, Rachel, Natalie and Risa jointly contributed to the cost of a present for their brother. Fiona's contribution is
35 of the total contribution made by the four girls. The ratio of Risa's contribution to the total of Rachel's and Natalie's contribution is 5 : 1. What is the total contribution by the four girls if Rachel's contribution is
14 of Natalie's contribution and the total amount contributed by Fiona and Risa is $140?
Fiona |
Rachel |
Natalie |
Risa |
Total |
3x15 |
2x15 |
5x15 |
|
1x5
|
5x5 |
|
|
1x1 |
4x1 |
|
|
45 u |
1 u |
4 u |
25 u |
75 u |
Working backwards.
Total amount that Rachel and Natalie had is the combined repeated identity.
LCM of 1 and 5 = 5
Total amount that Rachel, Natalie and Risa had is the next combined repeated identity.
LCM of 2 and 15 = 30
Total amount contributed by Fiona and Risa
= 45 u + 25 u
= 70 u
70 u = 140
1 u = 140 ÷ 70 = $2
Total contribution by the four girls
= 75 u
= 75 x 2
= $150
Answer(s): $150