There were 120 grapefruits and persimmons altogether. After
67 of the grapefruits and half of the persimmons were sold, there were a total of 30 grapefruits and persimmons left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
| |
Grapefruits |
Persimmons |
Total |
| Before |
7 u |
2 p |
120 |
| Change |
- 6 u |
- 1 p |
- 90 |
| After |
1 u |
1 p |
30 |
Number of grapefruits and persimmons sold
= 120 - 30
= 90
6 u + 1 p = 90
1 p = 90 - 6 u --- (1)
1 u + 1 p = 30
1 p = 30 - 1 u --- (2)
(2) = (1)
30 - 1 u = 90 - 6 u
6 u - 1 u = 90 - 30
5 u = 60
1 u = 60 ÷ 5 = 12
Number of grapefruits at first
= 7 u
= 7 x 12
= 84
Fraction of the fruits that were grapefruits at first
=
84120 =
710 Answer(s):
710 
