Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Leah owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 5 small tiers and 3 large tiers, which will serve a total of 248 guests. The second one includes 2 small tiers and 1 large tier, which is enough servings for 89 guests. How many guests does each size of tier serve? A small tier will serve _____ guests and a large tier will serve _____ guests.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Leah owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 5 small tiers and  3 large tiers, which will serve a total of 248 guests. The second one includes 2 small tiers and  1 large tier, which is enough servings for 89 guests. How many guests does each size of tier serve?  A small tier will serve _____ guests and a large tier will serve _____ guests.

Bytelearn · Accepted Answer

Set up equations: Set up the system of equations based on the given information. Leah's first cake has 5 small tiers and 3 large tiers serving 248 guests. Let's denote the number of guests served by a small tier as s and by a large tier as l. The equation for the first cake is: 5s + 3l = 248 The second cake has 2 small tiers and 1 large tier serving 89 guests. The equation for the second cake is: 2s + 1l = 89 Our system of equations is: 5s + 3l = 248 2s + 1l = 89Elimination method: Solve the system of equations using the elimination method. To eliminate one of the variables, we can multiply the second equation by 3 to match the coefficient of l in the first equation: 3(2s + 1l) = 3(89) 6s + 3l = 267 Now we have: 5s + 3l = 248 6s + 3l = 267 Subtract the first equation from the second equation to solve for s: (6s + 3l) - (5s + 3l) = 267 - 248 6s - 5s + 3l - 3l = 267 - 248 s = 19Solve for s: Substitute the value of s into one of the original equations to solve for l. Using the second equation 2s + l = 89, we substitute s = 19: 2(19) + l = 89 38 + l = 89 l = 89 - 38 l = 51Substitute and solve: Verify the solution by substituting the values of s and l into the other equation. Using the first equation 5s + 3l = 248, we substitute s = 19 and l = 51: 5(19) + 3(51) = 248 95 + 153 = 248 248 = 248 The values s = 19 and l = 51 satisfy both equations.

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