Gem had some red and gold beads. If she gives away 18 red beads, the number of red beads will be 20% of the total number of beads left. If she gives away 42 gold beads, the number of red beads will be 25% of the total number of beads left.
- How many beads does Gem have altogether?
- What fraction of Gem's beads is gold?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Gold |
Red |
Gold |
| Before |
1 u + 18 |
4 u |
1 p |
3 p + 42 |
| Change |
- 18 |
No change |
No change |
- 42 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 18 = 1 p --- (1)
4 u = 3 p + 42
4 u - 42 = 3 p --- (2)
Make p the same.
(1)
x33 u + 54 = 3 p --- (3)
(2) = (3)
4 u - 42 = 3 u + 54
4 u - 3 u = 54 + 42
1 u = 96
Number of beads that Gem had at first
= 1 u + 18 + 4 u
= 5 u + 18
= 5 x 96 + 18
= 480 + 18
= 498
(b)
Number of gold beads
= 4 u
= 4 x 96
= 384
Fraction of Gem's beads that is gold
=
384498=
6483 Answer(s): (a) 498; (b)
6483 
