A convenience store sold club, tuna and egg mayo sandwiches. The ratio of the number of club sandwiches made to the total number of sandwiches made was 3 : 7. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 1 : 5. After the store sold some club sandwiches and made another 5 tuna sandwiches, there was an equal number of club, tuna and egg mayo sandwiches left. Find the number of club sandwiches sold.
|
Club |
Tuna |
Egg Mayo |
Total |
Comparing club to total |
3x5 |
|
|
7x5 |
Comparing tuna to total |
|
1x7 |
|
5x7 |
|
15 u |
7 u |
13 u |
35 u |
|
Club |
Tuna |
Egg Mayo |
Total |
Before |
15 u |
7 u |
13 u |
35 u |
Change |
- 2 u |
+ 5 |
No change |
|
After |
1x13 = 13 u |
1x13 = 13 u |
1x13 = 13 u |
|
The total number of sandwiches is the same at first. Make the total number of sandwiches the same. LCM of 5 and 7 is 35.
Number of egg mayo sandwiches remains the same at first and in the end. Make the number of egg mayo sandwiches the same. LCM of 1 and 13 is 13.
Number of egg mayo sandwiches
= 35 u - 15 u - 7 u
= 13 u
Number of club, tuna and egg mayo sandwiches is the same in the end.
Number of tuna sandwiches = 7 u + 5
7 u + 5 = 13 u
13 u - 7 u = 5
6 u = 5
1 u = 5 ÷ 6 = 4
Number of club sandwiches sold
= 15 u - 13 u
= 2 u
= 2 x 4
= 8
Answer(s): 8