There were 116 persimmons and grapefruits altogether. After
45 of the persimmons and half of the grapefruits were sold, there were a total of 43 persimmons and grapefruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
| |
Persimmons |
Grapefruits |
Total |
| Before |
5 u |
2 p |
116 |
| Change |
- 4 u |
- 1 p |
- 73 |
| After |
1 u |
1 p |
43 |
Number of persimmons and grapefruits sold
= 116 - 43
= 73
4 u + 1 p = 73
1 p = 73 - 4 u --- (1)
1 u + 1 p = 43
1 p = 43 - 1 u --- (2)
(2) = (1)
43 - 1 u = 73 - 4 u
4 u - 1 u = 73 - 43
3 u = 30
1 u = 30 ÷ 3 = 10
Number of persimmons at first
= 5 u
= 5 x 10
= 50
Number of grapefruits at first
= 116 - 50
= 66
Fraction of the fruits that were grapefruits at first
=
66116 =
3358 Answer(s):
3358 
