Emma had a total of 247 purple and white marbles. She used
35 of her purple marbles and bought another 59 white marbles. The number of white marbles she had then become
13 the number of purple marbles. How many less white marbles than purple marbles did she have at first?
| |
Purple marbles |
White marbles |
| Before |
5x3 |
|
| Change |
- 3x3 |
+ 59 |
| After |
2x3 |
|
| Comparing marbles in the end |
3x2 |
1x2 |
| |
Purple marbles |
White marbles |
| Before |
15 u |
2 u - 59 |
| Change |
- 9 u |
+ 59 |
| After |
6 u |
2 u |
The number of purple marbles in the end is repeated.
LCM of 2 and 3 is 6.
Total number of purple marbles and white marbles
= 15 u + 2 u - 59
= 17 u - 59
17 u - 59 = 247
17 u = 247 + 59
17 u = 306
1 u = 306 ÷ 17 = 18
Number of less white marbles than purple marbles at first
= 15 u - (2 u - 59)
= 13 u + 59
= 13 x 18 + 59
= 293
Answer(s): 293
