Penelope had a total of 326 black and red marbles. She used
45 of her black marbles and bought another 31 red marbles. The number of red marbles she had then become
14 the number of black marbles. How many less red marbles than black marbles did she have at first?
|
Black marbles |
Red marbles |
Before |
5x4 |
|
Change |
- 4x4 |
+ 31 |
After |
1x4 |
|
Comparing marbles in the end |
4x1 |
1x1 |
|
Black marbles |
Red marbles |
Before |
20 u |
1 u - 31 |
Change |
- 16 u |
+ 31 |
After |
4 u |
1 u |
The number of black marbles in the end is repeated.
LCM of 1 and 4 is 4.
Total number of black marbles and red marbles
= 20 u + 1 u - 31
= 21 u - 31
21 u - 31 = 326
21 u = 326 + 31
21 u = 357
1 u = 357 ÷ 21 = 17
Number of less red marbles than black marbles at first
= 20 u - (1 u - 31)
= 19 u + 31
= 19 x 17 + 31
= 354
Answer(s): 354