There were 114 grapefruits and mangosteens altogether. After
34 of the grapefruits and half of the mangosteens were thrown away, there were a total of 36 grapefruits and mangosteens left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
|
Grapefruits |
Mangosteens |
Total |
Before |
4 u |
2 p |
114 |
Change |
- 3 u |
- 1 p |
- 78 |
After |
1 u |
1 p |
36 |
Number of grapefruits and mangosteens thrown away
= 114 - 36
= 78
3 u + 1 p = 78
1 p = 78 - 3 u --- (1)
1 u + 1 p = 36
1 p = 36 - 1 u --- (2)
(2) = (1)
36 - 1 u = 78 - 3 u
3 u - 1 u = 78 - 36
2 u = 42
1 u = 42 ÷ 2 = 21
Number of grapefruits at first
= 4 u
= 4 x 21
= 84
Fraction of the fruits that were grapefruits at first
=
84114 =
1419 Answer(s):
1419