A convenience store sold ham, tuna and chicken 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 tuna sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some ham sandwiches and made another 25 tuna sandwiches, there was an equal number of ham, tuna and chicken sandwiches left. Find the number of ham sandwiches sold.
|
Ham |
Tuna |
Chicken |
Total |
Comparing ham to total |
1x9 |
|
|
2x9 |
Comparing tuna to total |
|
1x2 |
|
9x2 |
|
9 u |
2 u |
7 u |
18 u |
|
Ham |
Tuna |
Chicken |
Total |
Before |
9 u |
2 u |
7 u |
18 u |
Change |
- 2 u |
+ 25 |
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 chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the same. LCM of 1 and 7 is 7.
Number of chicken sandwiches
= 18 u - 9 u - 2 u
= 7 u
Number of ham, tuna and chicken sandwiches is the same in the end.
Number of tuna sandwiches = 2 u + 25
2 u + 25 = 7 u
7 u - 2 u = 25
5 u = 25
1 u = 25 ÷ 5 = 6
Number of ham sandwiches sold
= 9 u - 7 u
= 2 u
= 2 x 6
= 12
Answer(s): 12