Adam has some red stickers and blue stickers.
If 42 red stickers are removed, 80% of the stickers will be blue stickers.
If 108 red stickers are added, 30% of the stickers will be blue stickers.
- How many red stickers are there?
- How many blue stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Red |
Blue |
Red |
Blue |
Before |
3 u + 42 |
12 u |
28 u - 108 |
12 u |
Change |
- 42 |
No change |
+ 108 |
No change |
After |
1x3 = 3 u |
4x3 = 12 u |
7x4 = 28 u |
3x4 = 12 u |
(a)
80% =
80100 =
4530% =
30100 =
310Scenario 1 Fraction of the stickers that are red in the end
= 1 -
45 =
15 Scenario 2
Fraction of the stickers that are red in the end
= 1 -
310 =
710 The number of blue stickers remains unchanged in both scenarios.
LCM of 4 and 3 = 12
28 u - 108 = 3 u + 42
28 u - 3 u = 42 + 108
25 u = 150
1 u = 150 ÷ 25 = 6
Number of red stickers
= 3 u + 42
= 3 x 6 + 42
= 18 + 42
= 60
(b)
Number of blue stickers
= 12 u
= 12 x 6
= 72
Answer(s): (a) 60; (b) 72