Final answer:
By setting up a system of equations and solving for the number of guests each tier serves, we find that a small tier serves 20 guests and a medium tier serves 40; therefore, in total, they serve 60 guests.
Step-by-step explanation:
To determine how many guests a small tier and a medium tier will serve in total for Laneka's cakes, we need to set up a system of equations. For the first cake, which serves 100 guests, we have 3 small tiers (S) and 1 medium tier (M) which can be represented as:
3S + M = 100
For the second cake, which serves 140 guests, we have 3 small tiers (S) and 2 medium tiers (M) which can be written as:
3S + 2M = 140
To solve these equations, we can multiply the first equation by 2 to eliminate the medium tier variable:
2(3S + M) = 2(100)
6S + 2M = 200
We then subtract the second equation from this result:
6S + 2M - (3S + 2M) = 200 - 140
3S = 60
This simplifies to S = 20, which means each small tier serves 20 guests. Substituting S into the first equation:
3(20) + M = 100
60 + M = 100
M = 40, which means each medium tier serves 40 guests.
The total number of guests served by one small tier and one medium tier is 20 guests for the small tier plus 40 guests for the medium tier, giving us:
20 + 40 = 60.
Hence, the correct answer is C. 60.