A convenience store sold egg mayo, salmon and club sandwiches. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 4 : 7. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some egg mayo sandwiches and made another 29 salmon sandwiches, there was an equal number of egg mayo, salmon and club sandwiches left. Find the number of egg mayo sandwiches sold.
|
Egg Mayo |
Salmon |
Club |
Total |
Comparing egg mayo to total |
4x9 |
|
|
7x9 |
Comparing salmon to total |
|
1x7 |
|
9x7 |
|
36 u |
7 u |
20 u |
63 u |
|
Egg Mayo |
Salmon |
Club |
Total |
Before |
36 u |
7 u |
20 u |
63 u |
Change |
- 16 u |
+ 29 |
No change |
|
After |
1x20 = 20 u |
1x20 = 20 u |
1x20 = 20 u |
|
The total number of sandwiches is the same at first. Make the total number of sandwiches the same. LCM of 9 and 7 is 63.
Number of club sandwiches remains the same at first and in the end. Make the number of club sandwiches the same. LCM of 1 and 20 is 20.
Number of club sandwiches
= 63 u - 36 u - 7 u
= 20 u
Number of egg mayo, salmon and club sandwiches is the same in the end.
Number of salmon sandwiches = 7 u + 29
7 u + 29 = 20 u
20 u - 7 u = 29
13 u = 29
1 u = 29 ÷ 13 = 8
Number of egg mayo sandwiches sold
= 36 u - 20 u
= 16 u
= 16 x 8
= 128
Answer(s): 128