Adam has 342 red marbles.
He has 6 times as many red marbles as blue marbles.
After he buys an equal number of red and blue marbles,
the number of red marbles is 4 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 buy?
|
Red marbles |
Blue marbles |
Difference |
Before |
6 x 3 = 18 u |
1 x 3 = 3 u |
5 x 3 = 15 u |
Change |
+ ? |
+ ? |
|
After |
4 x 5 = 20 u |
1 x 5 = 5 u |
3 x 5 = 15 u |
(a)
The difference in the number between the red and blue marbles at first and in the end remains unchanged.
LCM of 5 and 3 is 15.
18 u = 342
1 u = 342 ÷ 18 = 19
Number of red marbles in the end
= 20 u
= 20 x 19
= 380
(b)
Number of blue marbles in the end
= 5 u
= 5 x 19
= 95
(c)
Total number of marbles in the end
= 380 + 95
= 475
(d)
Total number of marbles that Adam buys
= (20 u - 18 u) x 2
= 2 u x 2
= 4 u
= 4 x 19
= 76
Answer(s): (a) 380; (b) 95; (c) 475; (d) 76