Adam has some red stickers and blue stickers.
If 45 red stickers are added, 70% of the stickers will be blue stickers.
If 325 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 |
9 u - 45 |
21 u |
49 u - 325 |
21 u |
Change |
+ 45 |
No change |
+ 325 |
No change |
After |
3x3 = 9 u |
7x3 = 21 u |
7x7 = 49 u |
3x7 = 21 u |
(a)
70% =
70100 =
71030% =
30100 =
310 Scenario 1 Fraction of the stickers that are red in the end
= 1 -
710 =
310 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 7 and 3 = 21
49 u - 325 = 9 u - 45
49 u - 9 u = 325 - 45
40 u = 280
1 u = 280 ÷ 40 = 7
Number of red stickers
= 9 u - 45
= 9 x 7 - 45
= 63 - 45
= 18
(b)
Number of blue stickers
= 21 u
= 21 x 7
= 147
Answer(s): (a) 18; (b) 147