A convenience store sold ham, egg mayo and bacon sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some ham sandwiches and made another 13 egg mayo sandwiches, there was an equal number of ham, egg mayo and bacon sandwiches left. Find the number of ham sandwiches sold.
|
Ham |
Egg Mayo |
Bacon |
Total |
Comparing ham to total |
1x9 |
|
|
2x9 |
Comparing egg mayo to total |
|
1x2 |
|
9x2 |
|
9 u |
2 u |
7 u |
18 u |
|
Ham |
Egg Mayo |
Bacon |
Total |
Before |
9 u |
2 u |
7 u |
18 u |
Change |
- 2 u |
+ 13 |
No change |
|
After |
1x7 = 7 u |
1x7 = 7 u |
1x7 = 7 u |
|
The total number of sandwiches is the same at first. Make the total number of sandwiches the same. LCM of 9 and 2 is 18.
Number of bacon sandwiches remains the same at first and in the end. Make the number of bacon sandwiches the same. LCM of 1 and 7 is 7.
Number of bacon sandwiches
= 18 u - 9 u - 2 u
= 7 u
Number of ham, egg mayo and bacon sandwiches is the same in the end.
Number of egg mayo sandwiches = 2 u + 13
2 u + 13 = 7 u
7 u - 2 u = 13
5 u = 13
1 u = 13 ÷ 5 = 5
Number of ham sandwiches sold
= 9 u - 7 u
= 2 u
= 2 x 5
= 10
Answer(s): 10