There were 112 grapefruits and mangosteens altogether. After
56 of the grapefruits and half of the mangosteens were given away, there were a total of 30 grapefruits and mangosteens left. What fraction of the fruits were mangosteens at first? Give your answer in its simplest form.
| |
Grapefruits |
Mangosteens |
Total |
| Before |
6 u |
2 p |
112 |
| Change |
- 5 u |
- 1 p |
- 82 |
| After |
1 u |
1 p |
30 |
Number of grapefruits and mangosteens given away
= 112 - 30
= 82
5 u + 1 p = 82
1 p = 82 - 5 u --- (1)
1 u + 1 p = 30
1 p = 30 - 1 u --- (2)
(2) = (1)
30 - 1 u = 82 - 5 u
5 u - 1 u = 82 - 30
4 u = 52
1 u = 52 ÷ 4 = 13
Number of grapefruits at first
= 6 u
= 6 x 13
= 78
Number of mangosteens at first
= 112 - 78
= 34
Fraction of the fruits that were mangosteens at first
=
34112 =
1756 Answer(s):
1756 
