There were 112 grapefruits and dragonfruits altogether. After
34 of the grapefruits and half of the dragonfruits were thrown away, there were a total of 42 grapefruits and dragonfruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
|
Grapefruits |
Dragonfruits |
Total |
Before |
4 u |
2 p |
112 |
Change |
- 3 u |
- 1 p |
- 70 |
After |
1 u |
1 p |
42 |
Number of grapefruits and dragonfruits thrown away
= 112 - 42
= 70
3 u + 1 p = 70
1 p = 70 - 3 u --- (1)
1 u + 1 p = 42
1 p = 42 - 1 u --- (2)
(2) = (1)
42 - 1 u = 70 - 3 u
3 u - 1 u = 70 - 42
2 u = 28
1 u = 28 ÷ 2 = 14
Number of grapefruits at first
= 4 u
= 4 x 14
= 56
Fraction of the fruits that were grapefruits at first
=
56112 =
12 Answer(s):
12