Answer: Hope this helps
Explanation:
Let ss be the number of guests that a small tier can serve and mm be the number of guests a medium tier can serve.
The first cake has 3 small tiers, which will serve 3s3s people, and one medium tier, which will serve mm people. The first cake can then serve 3s+m3s+m people. Since the first cake will serve 100 guests, then 3s+m=1003s+m=100.
The second cake has 3 small tiers, which will serve 3s3s people, and 2 medium tiers, which will serve 2m2m people. The second cake can then serve 3s+2m3s+2m people. Since the second cake will serve 140 guests, then 3s+2m=1403s+2m=140.
The system of equations is then { 3s+m=100 3s+2m=140
{
3s+m=100
3s+2m=140
Part B:
The mm-terms have the same coefficients so subtract the first equation from the second equation to eliminate ss and solve for mm:
3s+2m amp;= amp;140 −(3s+m amp;= amp;100) m amp;= amp;40
3s+2m
−(3s+m
m
amp;=
amp;=
amp;=
amp;140
amp;100)
amp;40
Substitute m=40m=40 into either equation and solve for ss:
3s+m amp;=100 3s+40 amp;=100 3s amp;=60 s amp;=20
3s+m
3s+40
3s
s
amp;=100
amp;=100
amp;=60
amp;=20
The solution of the system is then (s,m)=(20,40)
(s,m)=(20,40)
.
Part C:
Since the solution of the system was s=20s=20 and m=40m=40, then a small tier feeds 20 people and a medium teir serves 40 people.