Linda had some pink and gold beads. If she gives away 25 pink beads, the number of pink beads will be 20% of the total number of beads left. If she gives away 15 gold beads, the number of pink beads will be 25% of the total number of beads left.
- How many beads does Linda have altogether?
- What fraction of Linda's beads is gold?
| |
Scenario 1 |
Scenario 2 |
| |
Pink |
Gold |
Pink |
Gold |
| Before |
1 u + 25 |
4 u |
1 p |
3 p + 15 |
| Change |
- 25 |
No change |
No change |
- 15 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 25 = 1 p --- (1)
4 u = 3 p + 15
4 u - 15 = 3 p --- (2)
Make p the same.
(1)
x33 u + 75 = 3 p --- (3)
(2) = (3)
4 u - 15 = 3 u + 75
4 u - 3 u = 75 + 15
1 u = 90
Number of beads that Linda had at first
= 1 u + 25 + 4 u
= 5 u + 25
= 5 x 90 + 25
= 450 + 25
= 475
(b)
Number of gold beads
= 4 u
= 4 x 90
= 360
Fraction of Linda's beads that is gold
=
360475=
7295 Answer(s): (a) 475; (b)
7295 
