Jean had some yellow and silver marbles. If she gives away 20 yellow marbles, the number of yellow marbles will be 20% of the total number of marbles left. If she gives away 30 silver marbles, the number of yellow marbles will be 25% of the total number of marbles left.
- How many marbles does Jean have altogether?
- What fraction of Jean's marbles is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Yellow |
Silver |
Yellow |
Silver |
| Before |
1 u + 20 |
4 u |
1 p |
3 p + 30 |
| Change |
- 20 |
No change |
No change |
- 30 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 20 = 1 p --- (1)
4 u = 3 p + 30
4 u - 30 = 3 p --- (2)
Make p the same.
(1)
x33 u + 60 = 3 p --- (3)
(2) = (3)
4 u - 30 = 3 u + 60
4 u - 3 u = 60 + 30
1 u = 90
Number of marbles that Jean had at first
= 1 u + 20 + 4 u
= 5 u + 20
= 5 x 90 + 20
= 450 + 20
= 470
(b)
Number of silver marbles
= 4 u
= 4 x 90
= 360
Fraction of Jean's marbles that is silver
=
360470=
3647 Answer(s): (a) 470; (b)
3647 
