Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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.

Sagot :

sqdancefan

Answer:

  • small tier: 22
  • large tier: 50

Step-by-step 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.

View image sqdancefan
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.