Gabby had some red and brown balls. If she gives away 36 red balls, the number of red balls will be 10% of the total number of balls left. If she gives away 18 brown balls, the number of red balls will be 25% of the total number of balls left.
- How many balls does Gabby have altogether?
- What fraction of Gabby's balls is brown?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Brown |
Red |
Brown |
| Before |
1 u + 36 |
9 u |
1 p |
3 p + 18 |
| Change |
- 36 |
No change |
No change |
- 18 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 36 = 1 p --- (1)
9 u = 3 p + 18
9 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 108 = 3 p --- (3)
(2) = (3)
9 u - 18 = 3 u + 108
9 u - 3 u = 108 + 18
6 u = 126
1 u = 126 ÷ 6 = 21
Number of balls that Gabby had at first
= 1 u + 36 + 9 u
= 10 u + 36
= 10 x 21 + 36
= 210 + 36
= 246
(b)
Number of brown balls
= 9 u
= 9 x 21
= 189
Fraction of Gabby's balls that is brown
=
189246=
6382 Answer(s): (a) 246; (b)
6382 
