Lucy had some blue and green marbles. If she gives away 32 blue marbles, the number of blue marbles will be 10% of the total number of marbles left. If she gives away 18 green marbles, the number of blue marbles will be 25% of the total number of marbles left.
- How many marbles does Lucy have altogether?
- What fraction of Lucy's marbles is green?
|
Scenario 1 |
Scenario 2 |
|
Blue |
Green |
Blue |
Green |
Before |
1 u + 32 |
9 u |
1 p |
3 p + 18 |
Change |
- 32 |
No change |
No change |
- 18 |
After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 32 = 1 p --- (1)
9 u = 3 p + 18
9 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 96 = 3 p --- (3)
(2) = (3)
9 u - 18 = 3 u + 96
9 u - 3 u = 96 + 18
6 u = 114
1 u = 114 ÷ 6 = 19
Number of marbles that Lucy had at first
= 1 u + 32 + 9 u
= 10 u + 32
= 10 x 19 + 32
= 190 + 32
= 222
(b)
Number of green marbles
= 9 u
= 9 x 19
= 171
Fraction of Lucy's marbles that is green
=
171222=
5774 Answer(s): (a) 222; (b)
5774