There were 102 grapefruits and passion fruits altogether. After
34 of the grapefruits and half of the passion fruits were given away, there were a total of 27 grapefruits and passion fruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
|
Grapefruits |
Passion Fruits |
Total |
Before |
4 u |
2 p |
102 |
Change |
- 3 u |
- 1 p |
- 75 |
After |
1 u |
1 p |
27 |
Number of grapefruits and passion fruits given away
= 102 - 27
= 75
3 u + 1 p = 75
1 p = 75 - 3 u --- (1)
1 u + 1 p = 27
1 p = 27 - 1 u --- (2)
(2) = (1)
27 - 1 u = 75 - 3 u
3 u - 1 u = 75 - 27
2 u = 48
1 u = 48 ÷ 2 = 24
Number of grapefruits at first
= 4 u
= 4 x 24
= 96
Fraction of the fruits that were grapefruits at first
=
96102 =
1617 Answer(s):
1617