Shiyun had a total of 244 red and purple marbles. She used
37 of her red marbles and bought another 31 purple marbles. The number of purple marbles she had then become
13 the number of red marbles. How many less purple marbles than red marbles did she have at first?
|
Red marbles |
Purple marbles |
Before |
7x3 |
|
Change |
- 3x3 |
+ 31 |
After |
4x3 |
|
Comparing marbles in the end |
3x4 |
1x4 |
|
Red marbles |
Purple marbles |
Before |
21 u |
4 u - 31 |
Change |
- 9 u |
+ 31 |
After |
12 u |
4 u |
The number of red marbles in the end is repeated.
LCM of 4 and 3 is 12.
Total number of red marbles and purple marbles
= 21 u + 4 u - 31
= 25 u - 31
25 u - 31 = 244
25 u = 244 + 31
25 u = 275
1 u = 275 ÷ 25 = 11
Number of less purple marbles than red marbles at first
= 21 u - (4 u - 31)
= 17 u + 31
= 17 x 11 + 31
= 218
Answer(s): 218