Jane had some brown and silver beads. If she gives away 24 brown beads, the number of brown beads will be 20% of the total number of beads left. If she gives away 42 silver beads, the number of brown beads will be 25% of the total number of beads left.
- How many beads does Jane have altogether?
- What fraction of Jane's beads is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
Silver |
Brown |
Silver |
| Before |
1 u + 24 |
4 u |
1 p |
3 p + 42 |
| Change |
- 24 |
No change |
No change |
- 42 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 24 = 1 p --- (1)
4 u = 3 p + 42
4 u - 42 = 3 p --- (2)
Make p the same.
(1)
x33 u + 72 = 3 p --- (3)
(2) = (3)
4 u - 42 = 3 u + 72
4 u - 3 u = 72 + 42
1 u = 114
Number of beads that Jane had at first
= 1 u + 24 + 4 u
= 5 u + 24
= 5 x 114 + 24
= 570 + 24
= 594
(b)
Number of silver beads
= 4 u
= 4 x 114
= 456
Fraction of Jane's beads that is silver
=
456594=
7699 Answer(s): (a) 594; (b)
7699 
