Adam has some blue stickers and red stickers.
If 103 blue stickers are added, 40% of the stickers will be red stickers.
If 348 red stickers are added, 10% of the stickers will be blue stickers.
- How many blue stickers are there?
- How many red stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Blue |
Red |
Blue |
Red |
Before |
3 u - 103 |
2 u |
1 p |
9 p - 348 |
Change |
+ 103 |
No change |
No change |
+ 348 |
After |
3 u |
2 u |
1 p |
9 p |
(a)
40% =
40100 =
25 10% =
10100 =
110 Scenario 1 Fraction of the stickers that are blue
= 1 -
25 =
35 Number of blue stickers at first = 3 u - 103
Number of red stickers at first = 2 u
Scenario 2 Fraction of the stickers that are red
= 1 -
110=
910 Number of blue stickers at first = 1 p
Number of red stickers at first = 9 p - 348
3 u - 103 = 1 p --- (1)
2 u = 9 p - 348
2 u + 348 = 9 p --- (2)
(1)
x 9 27 u - 927 = 9 p --- (3)
(3) = (2)
27 u - 927 = 2 u + 348
27 u - 2 u = 927 + 348
25 u = 1275
1 u = 1275 ÷ 25 = 51
Number of blue stickers
= 3 u - 103
= 3 x 51 - 103
= 153 - 103
= 50
(b)
Number of red stickers
= 2 u
= 2 x 51
= 102
Answer(s): (a) 50; (b) 102