A convenience store sold ham, chicken and bacon sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 4 : 9. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some ham sandwiches and made another 5 chicken sandwiches, there was an equal number of ham, chicken and bacon sandwiches left. Find the number of ham sandwiches sold.
|
Ham |
Chicken |
Bacon |
Total |
Comparing ham to total |
4x7 |
|
|
9x7 |
Comparing chicken to total |
|
1x9 |
|
7x9 |
|
28 u |
9 u |
26 u |
63 u |
|
Ham |
Chicken |
Bacon |
Total |
Before |
28 u |
9 u |
26 u |
63 u |
Change |
- 2 u |
+ 5 |
No change |
|
After |
1x26 = 26 u |
1x26 = 26 u |
1x26 = 26 u |
|
The total number of sandwiches is the same at first. Make the total number of sandwiches the same. LCM of 7 and 9 is 63.
Number of bacon sandwiches remains the same at first and in the end. Make the number of bacon sandwiches the same. LCM of 1 and 26 is 26.
Number of bacon sandwiches
= 63 u - 28 u - 9 u
= 26 u
Number of ham, chicken and bacon sandwiches is the same in the end.
Number of chicken sandwiches = 9 u + 5
9 u + 5 = 26 u
26 u - 9 u = 5
17 u = 5
1 u = 5 ÷ 17 = 6
Number of ham sandwiches sold
= 28 u - 26 u
= 2 u
= 2 x 6
= 12
Answer(s): 12