Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Destiny owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 4 small tiers and 4 large tiers, which will serve a total of 288 guests. The second one includes 3 small tiers and 5 large tiers, which is enough servings for 316 guests. How many guests does each size of tier serve?

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

Answer 1

• small tier: 22
• large tier: 50

Explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Setup

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

4s +4l = 288

And the second cake serves ...

3s +5l = 316

Solution

Subtracting 3/4 of the first equation from the second gives ...

(3x +5l) -3/4(4s +4l) = (316) -3/4(288)

2l = 100

l = 50

4s +4(50) = 288 . . . substitute for l in the first equation

4s = 88 . . . . . . . . . . subtract 200

s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.