A convenience store sold chicken, tuna and egg mayo sandwiches. The ratio of the number of chicken 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 : 4. After the store sold some chicken sandwiches and made another 10 tuna sandwiches, there was an equal number of chicken, tuna and egg mayo sandwiches left. Find the number of chicken sandwiches sold.
|
Chicken |
Tuna |
Egg Mayo |
Total |
Comparing chicken to total |
3x4 |
|
|
7x4 |
Comparing tuna to total |
|
1x7 |
|
4x7 |
|
12 u |
7 u |
9 u |
28 u |
|
Chicken |
Tuna |
Egg Mayo |
Total |
Before |
12 u |
7 u |
9 u |
28 u |
Change |
- 3 u |
+ 10 |
No change |
|
After |
1x9 = 9 u |
1x9 = 9 u |
1x9 = 9 u |
|
The total number of sandwiches is the same at first. Make the total number of sandwiches the same. LCM of 4 and 7 is 28.
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 9 is 9.
Number of egg mayo sandwiches
= 28 u - 12 u - 7 u
= 9 u
Number of chicken, tuna and egg mayo sandwiches is the same in the end.
Number of tuna sandwiches = 7 u + 10
7 u + 10 = 9 u
9 u - 7 u = 10
2 u = 10
1 u = 10 ÷ 2 = 6
Number of chicken sandwiches sold
= 12 u - 9 u
= 3 u
= 3 x 6
= 18
Answer(s): 18