Adam has some blue stickers and red stickers.
If 82 blue stickers are added, 70% of the stickers will be red stickers.
If 367 blue stickers are added, 40% of the stickers will be red stickers.
- How many blue stickers are there?
- How many red stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Blue |
Red |
Blue |
Red |
Before |
6 u - 82 |
14 u |
21 u - 367 |
14 u |
Change |
+ 82 |
No change |
+ 367 |
No change |
After |
3x2 = 6 u |
7x2 = 14 u |
3x7 = 21 u |
2x7 = 14 u |
(a)
70% =
70100 =
71040% =
40100 =
25 Scenario 1 Fraction of the stickers that are blue in the end
= 1 -
710 =
310 Scenario 2
Fraction of the stickers that are blue in the end
= 1 -
25 =
35 The number of red stickers remains unchanged in both scenarios.
LCM of 7 and 2 = 14
21 u - 367 = 6 u - 82
21 u - 6 u = 367 - 82
15 u = 285
1 u = 285 ÷ 15 = 19
Number of blue stickers
= 6 u - 82
= 6 x 19 - 82
= 114 - 82
= 32
(b)
Number of red stickers
= 14 u
= 14 x 19
= 266
Answer(s): (a) 32; (b) 266