Wendy had some gold and blue balls. If she gives away 35 gold balls, the number of gold balls will be 10% of the total number of balls left. If she gives away 21 blue balls, the number of gold balls will be 25% of the total number of balls left.
- How many balls does Wendy have altogether?
- What fraction of Wendy's balls is blue?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Blue |
Gold |
Blue |
| Before |
1 u + 35 |
9 u |
1 p |
3 p + 21 |
| Change |
- 35 |
No change |
No change |
- 21 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 35 = 1 p --- (1)
9 u = 3 p + 21
9 u - 21 = 3 p --- (2)
Make p the same.
(1)
x33 u + 105 = 3 p --- (3)
(2) = (3)
9 u - 21 = 3 u + 105
9 u - 3 u = 105 + 21
6 u = 126
1 u = 126 ÷ 6 = 21
Number of balls that Wendy had at first
= 1 u + 35 + 9 u
= 10 u + 35
= 10 x 21 + 35
= 210 + 35
= 245
(b)
Number of blue balls
= 9 u
= 9 x 21
= 189
Fraction of Wendy's balls that is blue
=
189245=
2735 Answer(s): (a) 245; (b)
2735 
