1) Deb owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 5 small tiers and 3 medium tiers, which will serve a total of 252 guests. The
second one includes 1 small tier and 3 medium tiers, which is enough servings for 168
guests. How many guests does each size of tier serve?

A small tier will serve
guests and a large tier will serve guests.

Hope this helps

Step-by-step 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=1003s+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+2mamp;=amp;140−(3s+mamp;=amp;100)      mamp;=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+mamp;=1003s+40amp;=1003samp;=60samp;=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.

c. (3,2,6) is the answer.