Erika had some grey and pink beads. If she gives away 34 grey beads, the number of grey beads will be 10% of the total number of beads left. If she gives away 36 pink beads, the number of grey beads will be 25% of the total number of beads left.
- How many beads does Erika have altogether?
- What fraction of Erika's beads is pink?
| |
Scenario 1 |
Scenario 2 |
| |
Grey |
Pink |
Grey |
Pink |
| Before |
1 u + 34 |
9 u |
1 p |
3 p + 36 |
| Change |
- 34 |
No change |
No change |
- 36 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 34 = 1 p --- (1)
9 u = 3 p + 36
9 u - 36 = 3 p --- (2)
Make p the same.
(1)
x33 u + 102 = 3 p --- (3)
(2) = (3)
9 u - 36 = 3 u + 102
9 u - 3 u = 102 + 36
6 u = 138
1 u = 138 ÷ 6 = 23
Number of beads that Erika had at first
= 1 u + 34 + 9 u
= 10 u + 34
= 10 x 23 + 34
= 230 + 34
= 264
(b)
Number of pink beads
= 9 u
= 9 x 23
= 207
Fraction of Erika's beads that is pink
=
207264=
6988 Answer(s): (a) 264; (b)
6988 
