Tina had some gold and silver beads. If she gives away 41 gold beads, the number of gold beads will be 20% of the total number of beads left. If she gives away 41 silver beads, the number of gold beads will be 25% of the total number of beads left.
- How many beads does Tina have altogether?
- What fraction of Tina's beads is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Silver |
Gold |
Silver |
| Before |
1 u + 41 |
4 u |
1 p |
3 p + 41 |
| Change |
- 41 |
No change |
No change |
- 41 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 41 = 1 p --- (1)
4 u = 3 p + 41
4 u - 41 = 3 p --- (2)
Make p the same.
(1)
x33 u + 123 = 3 p --- (3)
(2) = (3)
4 u - 41 = 3 u + 123
4 u - 3 u = 123 + 41
1 u = 164
Number of beads that Tina had at first
= 1 u + 41 + 4 u
= 5 u + 41
= 5 x 164 + 41
= 820 + 41
= 861
(b)
Number of silver beads
= 4 u
= 4 x 164
= 656
Fraction of Tina's beads that is silver
=
656861=
1621 Answer(s): (a) 861; (b)
1621 
