Julie had a total of 337 gold and black marbles. She used
45 of her gold marbles and bought another 62 black marbles. The number of black marbles she had then become
14 the number of gold marbles. How many less black marbles than gold marbles did she have at first?
|
Gold marbles |
Black marbles |
Before |
5x4 |
|
Change |
- 4x4 |
+ 62 |
After |
1x4 |
|
Comparing marbles in the end |
4x1 |
1x1 |
|
Gold marbles |
Black marbles |
Before |
20 u |
1 u - 62 |
Change |
- 16 u |
+ 62 |
After |
4 u |
1 u |
The number of gold marbles in the end is repeated.
LCM of 1 and 4 is 4.
Total number of gold marbles and black marbles
= 20 u + 1 u - 62
= 21 u - 62
21 u - 62 = 337
21 u = 337 + 62
21 u = 399
1 u = 399 ÷ 21 = 19
Number of less black marbles than gold marbles at first
= 20 u - (1 u - 62)
= 19 u + 62
= 19 x 19 + 62
= 423
Answer(s): 423