Winnie had a total of 259 gold and purple marbles. She used
35 of her gold marbles and bought another 64 purple marbles. The number of purple marbles she had then become
13 the number of gold marbles. How many less purple marbles than gold marbles did she have at first?
| |
Gold marbles |
Purple marbles |
| Before |
5x3 |
|
| Change |
- 3x3 |
+ 64 |
| After |
2x3 |
|
| Comparing marbles in the end |
3x2 |
1x2 |
| |
Gold marbles |
Purple marbles |
| Before |
15 u |
2 u - 64 |
| Change |
- 9 u |
+ 64 |
| After |
6 u |
2 u |
The number of gold marbles in the end is repeated.
LCM of 2 and 3 is 6.
Total number of gold marbles and purple marbles
= 15 u + 2 u - 64
= 17 u - 64
17 u - 64 = 259
17 u = 259 + 64
17 u = 323
1 u = 323 ÷ 17 = 19
Number of less purple marbles than gold marbles at first
= 15 u - (2 u - 64)
= 13 u + 64
= 13 x 19 + 64
= 311
Answer(s): 311
