Julie had some green and black beads. If she gives away 10 green beads, the number of green beads will be 10% of the total number of beads left. If she gives away 36 black beads, the number of green beads will be 25% of the total number of beads left.
- How many beads does Julie have altogether?
- What fraction of Julie's beads is black?
| |
Scenario 1 |
Scenario 2 |
| |
Green |
Black |
Green |
Black |
| Before |
1 u + 10 |
9 u |
1 p |
3 p + 36 |
| Change |
- 10 |
No change |
No change |
- 36 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 10 = 1 p --- (1)
9 u = 3 p + 36
9 u - 36 = 3 p --- (2)
Make p the same.
(1)
x33 u + 30 = 3 p --- (3)
(2) = (3)
9 u - 36 = 3 u + 30
9 u - 3 u = 30 + 36
6 u = 66
1 u = 66 ÷ 6 = 11
Number of beads that Julie had at first
= 1 u + 10 + 9 u
= 10 u + 10
= 10 x 11 + 10
= 110 + 10
= 120
(b)
Number of black beads
= 9 u
= 9 x 11
= 99
Fraction of Julie's beads that is black
=
99120=
3340 Answer(s): (a) 120; (b)
3340 
