Xylia had some green and yellow balls. If she gives away 32 green balls, the number of green balls will be 10% of the total number of balls left. If she gives away 24 yellow balls, the number of green balls will be 25% of the total number of balls left.
- How many balls does Xylia have altogether?
- What fraction of Xylia's balls is yellow?
| |
Scenario 1 |
Scenario 2 |
| |
Green |
Yellow |
Green |
Yellow |
| Before |
1 u + 32 |
9 u |
1 p |
3 p + 24 |
| Change |
- 32 |
No change |
No change |
- 24 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 32 = 1 p --- (1)
9 u = 3 p + 24
9 u - 24 = 3 p --- (2)
Make p the same.
(1)
x33 u + 96 = 3 p --- (3)
(2) = (3)
9 u - 24 = 3 u + 96
9 u - 3 u = 96 + 24
6 u = 120
1 u = 120 ÷ 6 = 20
Number of balls that Xylia had at first
= 1 u + 32 + 9 u
= 10 u + 32
= 10 x 20 + 32
= 200 + 32
= 232
(b)
Number of yellow balls
= 9 u
= 9 x 20
= 180
Fraction of Xylia's balls that is yellow
=
180232=
4558 Answer(s): (a) 232; (b)
4558 
