A total of 21 gold files and red files are in a container. The ratio of gold files to red files was 1 : 6. Some purple files and yellow files were put into the container. For every 2 red files that were already in the container, 6 yellow ones were added. Then, the final number of gold files and purple files was
12 the final number of red files and yellow files. Find the total number of purple and yellow files.
| Purple files |
Gold files |
Red files |
Yellow files |
| |
1x1 |
6x1 |
|
| |
|
2x3 |
6x3 |
| 1x12 |
2x12 |
| 11 u |
1 u |
6 u |
18 u |
The number of red files is repeated. Make the number of red files the same. LCM of 6 and 2 is 6.
The total number of red files and yellow files is repeated. Make the total number of red and yellow files the same. LCM of 24 and 2 is 24.
Total number of gold files and red files
= 1 u + 6 u
= 7 u
7 u = 21
1 u = 21 ÷ 7 = 3
Total number of purple and yellow files
= 11 u + 18 u
= 29 u
= 29 x 3
= 87
Answer(s): 87
