A convenience store sold salmon, club and tuna sandwiches. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of club sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some salmon sandwiches and made another 9 club sandwiches, there was an equal number of salmon, club and tuna sandwiches left. Find the number of salmon sandwiches sold.
|
Salmon |
Club |
Tuna |
Total |
Comparing salmon to total |
1x9 |
|
|
2x9 |
Comparing club to total |
|
1x2 |
|
9x2 |
|
9 u |
2 u |
7 u |
18 u |
|
Salmon |
Club |
Tuna |
Total |
Before |
9 u |
2 u |
7 u |
18 u |
Change |
- 2 u |
+ 9 |
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 tuna sandwiches remains the same at first and in the end. Make the number of tuna sandwiches the same. LCM of 1 and 7 is 7.
Number of tuna sandwiches
= 18 u - 9 u - 2 u
= 7 u
Number of salmon, club and tuna sandwiches is the same in the end.
Number of club sandwiches = 2 u + 9
2 u + 9 = 7 u
7 u - 2 u = 9
5 u = 9
1 u = 9 ÷ 5 = 8
Number of salmon sandwiches sold
= 9 u - 7 u
= 2 u
= 2 x 8
= 16
Answer(s): 16