There were 140 pomegranates and grapefruits altogether. After
34 of the pomegranates and half of the grapefruits were given away, there were a total of 39 pomegranates and grapefruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
|
Pomegranates |
Grapefruits |
Total |
Before |
4 u |
2 p |
140 |
Change |
- 3 u |
- 1 p |
- 101 |
After |
1 u |
1 p |
39 |
Number of pomegranates and grapefruits given away
= 140 - 39
= 101
3 u + 1 p = 101
1 p = 101 - 3 u --- (1)
1 u + 1 p = 39
1 p = 39 - 1 u --- (2)
(2) = (1)
39 - 1 u = 101 - 3 u
3 u - 1 u = 101 - 39
2 u = 62
1 u = 62 ÷ 2 = 31
Number of pomegranates at first
= 4 u
= 4 x 31
= 124
Number of grapefruits at first
= 140 - 124
= 16
Fraction of the fruits that were grapefruits at first
=
16140 =
435 Answer(s):
435