Abi had some brown and silver balls. If she gives away 25 brown balls, the number of brown balls will be 20% of the total number of balls left. If she gives away 50 silver balls, the number of brown balls will be 25% of the total number of balls left.
- How many balls does Abi have altogether?
- What fraction of Abi's balls is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
Silver |
Brown |
Silver |
| Before |
1 u + 25 |
4 u |
1 p |
3 p + 50 |
| Change |
- 25 |
No change |
No change |
- 50 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 25 = 1 p --- (1)
4 u = 3 p + 50
4 u - 50 = 3 p --- (2)
Make p the same.
(1)
x33 u + 75 = 3 p --- (3)
(2) = (3)
4 u - 50 = 3 u + 75
4 u - 3 u = 75 + 50
1 u = 125
Number of balls that Abi had at first
= 1 u + 25 + 4 u
= 5 u + 25
= 5 x 125 + 25
= 625 + 25
= 650
(b)
Number of silver balls
= 4 u
= 4 x 125
= 500
Fraction of Abi's balls that is silver
=
500650=
1013 Answer(s): (a) 650; (b)
1013 
