Adam has 80 red marbles.
He has 4 times as many red marbles than blue marbles.
After he gives away an equal number of red and blue marbles,
the number of red marbles is 5 times that of the blue marbles.
- How many red marbles are there in the end?
- How many blue marbles are there in the end?
- How many marbles are there in the end?
- How many marbles does Adam give away?
|
Red marbles |
Blue marbles |
Difference |
Before |
4 x 4 = 16 u |
1 x 4 = 4 u |
3 x 4 = 12 u |
Change |
- ? |
- ? |
|
After |
5 x 3 = 15 u |
1 x 3 = 3 u |
4 x 3 = 12 u |
(a)
The difference in the number between the red and blue marbles at first and in the end remains unchanged.
LCM of 3 and 4 is 12.
16 u = 80
1 u = 80 ÷ 16 = 5
Number of red marbles in the end
= 15 u
= 15 x 5
= 75
(b)
Number of blue marbles in the end
= 3 u
= 3 x 5
= 15
(c)
Total number of marbles in the end
= 75 + 15
= 90
(d)
Total number of marbles that Adam gives away
= (16 u - 15 u) x 2
= 1 u x 2
= 2 u
= 2 x 5
= 10
Answer(s): (a) 75; (b) 15; (c) 90; (d) 10