Gwen had a total of 409 red and blue marbles. She used
45 of her red marbles and bought another 32 blue marbles. The number of blue marbles she had then become
14 the number of red marbles. How many less blue marbles than red marbles did she have at first?
| |
Red marbles |
Blue marbles |
| Before |
5x4 |
|
| Change |
- 4x4 |
+ 32 |
| After |
1x4 |
|
| Comparing marbles in the end |
4x1 |
1x1 |
| |
Red marbles |
Blue marbles |
| Before |
20 u |
1 u - 32 |
| Change |
- 16 u |
+ 32 |
| After |
4 u |
1 u |
The number of red marbles in the end is repeated.
LCM of 1 and 4 is 4.
Total number of red marbles and blue marbles
= 20 u + 1 u - 32
= 21 u - 32
21 u - 32 = 409
21 u = 409 + 32
21 u = 441
1 u = 441 ÷ 21 = 21
Number of less blue marbles than red marbles at first
= 20 u - (1 u - 32)
= 19 u + 32
= 19 x 21 + 32
= 431
Answer(s): 431
