Risa had some yellow and purple beads. If she gives away 13 yellow beads, the number of yellow beads will be 20% of the total number of beads left. If she gives away 32 purple beads, the number of yellow beads will be 25% of the total number of beads left.
- How many beads does Risa have altogether?
- What fraction of Risa's beads is purple?
| |
Scenario 1 |
Scenario 2 |
| |
Yellow |
Purple |
Yellow |
Purple |
| Before |
1 u + 13 |
4 u |
1 p |
3 p + 32 |
| Change |
- 13 |
No change |
No change |
- 32 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 13 = 1 p --- (1)
4 u = 3 p + 32
4 u - 32 = 3 p --- (2)
Make p the same.
(1)
x33 u + 39 = 3 p --- (3)
(2) = (3)
4 u - 32 = 3 u + 39
4 u - 3 u = 39 + 32
1 u = 71
Number of beads that Risa had at first
= 1 u + 13 + 4 u
= 5 u + 13
= 5 x 71 + 13
= 355 + 13
= 368
(b)
Number of purple beads
= 4 u
= 4 x 71
= 284
Fraction of Risa's beads that is purple
=
284368=
7192 Answer(s): (a) 368; (b)
7192 
