Jean had some red and yellow beads. If she gives away 20 red beads, the number of red beads will be 10% of the total number of beads left. If she gives away 18 yellow beads, the number of red beads will be 25% of the total number of beads left.
- How many beads does Jean have altogether?
- What fraction of Jean's beads is yellow?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Yellow |
Red |
Yellow |
| Before |
1 u + 20 |
9 u |
1 p |
3 p + 18 |
| Change |
- 20 |
No change |
No change |
- 18 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 20 = 1 p --- (1)
9 u = 3 p + 18
9 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 60 = 3 p --- (3)
(2) = (3)
9 u - 18 = 3 u + 60
9 u - 3 u = 60 + 18
6 u = 78
1 u = 78 ÷ 6 = 13
Number of beads that Jean had at first
= 1 u + 20 + 9 u
= 10 u + 20
= 10 x 13 + 20
= 130 + 20
= 150
(b)
Number of yellow beads
= 9 u
= 9 x 13
= 117
Fraction of Jean's beads that is yellow
=
117150=
3950 Answer(s): (a) 150; (b)
3950 
