Xuan had some yellow and gold beads. If she gives away 19 yellow beads, the number of yellow beads will be 20% of the total number of beads left. If she gives away 16 gold beads, the number of yellow beads will be 25% of the total number of beads left.
- How many beads does Xuan have altogether?
- What fraction of Xuan's beads is gold?
| |
Scenario 1 |
Scenario 2 |
| |
Yellow |
Gold |
Yellow |
Gold |
| Before |
1 u + 19 |
4 u |
1 p |
3 p + 16 |
| Change |
- 19 |
No change |
No change |
- 16 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 19 = 1 p --- (1)
4 u = 3 p + 16
4 u - 16 = 3 p --- (2)
Make p the same.
(1)
x33 u + 57 = 3 p --- (3)
(2) = (3)
4 u - 16 = 3 u + 57
4 u - 3 u = 57 + 16
1 u = 73
Number of beads that Xuan had at first
= 1 u + 19 + 4 u
= 5 u + 19
= 5 x 73 + 19
= 365 + 19
= 384
(b)
Number of gold beads
= 4 u
= 4 x 73
= 292
Fraction of Xuan's beads that is gold
=
292384=
7396 Answer(s): (a) 384; (b)
7396 
