Usha had some brown and yellow balls. If she gives away 15 brown balls, the number of brown balls will be 20% of the total number of balls left. If she gives away 12 yellow balls, the number of brown balls will be 25% of the total number of balls left.
- How many balls does Usha have altogether?
- What fraction of Usha's balls is yellow?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
Yellow |
Brown |
Yellow |
| Before |
1 u + 15 |
4 u |
1 p |
3 p + 12 |
| Change |
- 15 |
No change |
No change |
- 12 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 15 = 1 p --- (1)
4 u = 3 p + 12
4 u - 12 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
4 u - 12 = 3 u + 45
4 u - 3 u = 45 + 12
1 u = 57
Number of balls that Usha had at first
= 1 u + 15 + 4 u
= 5 u + 15
= 5 x 57 + 15
= 285 + 15
= 300
(b)
Number of yellow balls
= 4 u
= 4 x 57
= 228
Fraction of Usha's balls that is yellow
=
228300=
1925 Answer(s): (a) 300; (b)
1925 
