Yen had some white and grey beads. If she gives away 38 white beads, the number of white beads will be 20% of the total number of beads left. If she gives away 38 grey beads, the number of white beads will be 25% of the total number of beads left.
- How many beads does Yen have altogether?
- What fraction of Yen's beads is grey?
| |
Scenario 1 |
Scenario 2 |
| |
White |
Grey |
White |
Grey |
| Before |
1 u + 38 |
4 u |
1 p |
3 p + 38 |
| Change |
- 38 |
No change |
No change |
- 38 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 38 = 1 p --- (1)
4 u = 3 p + 38
4 u - 38 = 3 p --- (2)
Make p the same.
(1)
x33 u + 114 = 3 p --- (3)
(2) = (3)
4 u - 38 = 3 u + 114
4 u - 3 u = 114 + 38
1 u = 152
Number of beads that Yen had at first
= 1 u + 38 + 4 u
= 5 u + 38
= 5 x 152 + 38
= 760 + 38
= 798
(b)
Number of grey beads
= 4 u
= 4 x 152
= 608
Fraction of Yen's beads that is grey
=
608798=
1621 Answer(s): (a) 798; (b)
1621 
