There were 138 guavas and grapefruits altogether. After
56 of the guavas and half of the grapefruits were sold, there were a total of 33 guavas and grapefruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
| |
Guavas |
Grapefruits |
Total |
| Before |
6 u |
2 p |
138 |
| Change |
- 5 u |
- 1 p |
- 105 |
| After |
1 u |
1 p |
33 |
Number of guavas and grapefruits sold
= 138 - 33
= 105
5 u + 1 p = 105
1 p = 105 - 5 u --- (1)
1 u + 1 p = 33
1 p = 33 - 1 u --- (2)
(2) = (1)
33 - 1 u = 105 - 5 u
5 u - 1 u = 105 - 33
4 u = 72
1 u = 72 ÷ 4 = 18
Number of guavas at first
= 6 u
= 6 x 18
= 108
Number of grapefruits at first
= 138 - 108
= 30
Fraction of the fruits that were grapefruits at first
=
30138 =
523 Answer(s):
523 
