There were 111 mangosteens and grapefruits altogether. After
67 of the mangosteens and half of the grapefruits were thrown away, there were a total of 33 mangosteens and grapefruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
| |
Mangosteens |
Grapefruits |
Total |
| Before |
7 u |
2 p |
111 |
| Change |
- 6 u |
- 1 p |
- 78 |
| After |
1 u |
1 p |
33 |
Number of mangosteens and grapefruits thrown away
= 111 - 33
= 78
6 u + 1 p = 78
1 p = 78 - 6 u --- (1)
1 u + 1 p = 33
1 p = 33 - 1 u --- (2)
(2) = (1)
33 - 1 u = 78 - 6 u
6 u - 1 u = 78 - 33
5 u = 45
1 u = 45 ÷ 5 = 9
Number of mangosteens at first
= 7 u
= 7 x 9
= 63
Number of grapefruits at first
= 111 - 63
= 48
Fraction of the fruits that were grapefruits at first
=
48111 =
1637 Answer(s):
1637 
