Esther had some brown and white beads. If she gives away 50 brown beads, the number of brown beads will be 10% of the total number of beads left. If she gives away 30 white beads, the number of brown beads will be 25% of the total number of beads left.
- How many beads does Esther have altogether?
- What fraction of Esther's beads is white?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
White |
Brown |
White |
| Before |
1 u + 50 |
9 u |
1 p |
3 p + 30 |
| Change |
- 50 |
No change |
No change |
- 30 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 50 = 1 p --- (1)
9 u = 3 p + 30
9 u - 30 = 3 p --- (2)
Make p the same.
(1)
x33 u + 150 = 3 p --- (3)
(2) = (3)
9 u - 30 = 3 u + 150
9 u - 3 u = 150 + 30
6 u = 180
1 u = 180 ÷ 6 = 30
Number of beads that Esther had at first
= 1 u + 50 + 9 u
= 10 u + 50
= 10 x 30 + 50
= 300 + 50
= 350
(b)
Number of white beads
= 9 u
= 9 x 30
= 270
Fraction of Esther's beads that is white
=
270350=
2735 Answer(s): (a) 350; (b)
2735 
