Yen had some red and yellow marbles. If she gives away 20 red marbles, the number of red marbles will be 20% of the total number of marbles left. If she gives away 35 yellow marbles, the number of red marbles will be 25% of the total number of marbles left.
- How many marbles does Yen have altogether?
- What fraction of Yen's marbles is yellow?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Yellow |
Red |
Yellow |
| Before |
1 u + 20 |
4 u |
1 p |
3 p + 35 |
| Change |
- 20 |
No change |
No change |
- 35 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 20 = 1 p --- (1)
4 u = 3 p + 35
4 u - 35 = 3 p --- (2)
Make p the same.
(1)
x33 u + 60 = 3 p --- (3)
(2) = (3)
4 u - 35 = 3 u + 60
4 u - 3 u = 60 + 35
1 u = 95
Number of marbles that Yen had at first
= 1 u + 20 + 4 u
= 5 u + 20
= 5 x 95 + 20
= 475 + 20
= 495
(b)
Number of yellow marbles
= 4 u
= 4 x 95
= 380
Fraction of Yen's marbles that is yellow
=
380495=
7699 Answer(s): (a) 495; (b)
7699 
