There were 98 pears and grapefruits altogether. After
34 of the pears and half of the grapefruits were given away, there were a total of 42 pears and grapefruits left. What fraction of the fruits were grapefruits at first? Give your answer in its simplest form.
| |
Pears |
Grapefruits |
Total |
| Before |
4 u |
2 p |
98 |
| Change |
- 3 u |
- 1 p |
- 56 |
| After |
1 u |
1 p |
42 |
Number of pears and grapefruits given away
= 98 - 42
= 56
3 u + 1 p = 56
1 p = 56 - 3 u --- (1)
1 u + 1 p = 42
1 p = 42 - 1 u --- (2)
(2) = (1)
42 - 1 u = 56 - 3 u
3 u - 1 u = 56 - 42
2 u = 14
1 u = 14 ÷ 2 = 7
Number of pears at first
= 4 u
= 4 x 7
= 28
Number of grapefruits at first
= 98 - 28
= 70
Fraction of the fruits that were grapefruits at first
=
7098 =
57 Answer(s):
57 
