Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mrs. Coleman is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Norwood Florist charges $16 for each smaller arrangement, plus $33 for the large centerpiece. Adam's Flowers, in contrast, charges $41 for the large centerpiece and $8 per arrangement for the rest. If Mrs. Coleman orders a certain number of small arrangements, the cost will be the same at either flower shop. What would the total cost be? How many small arrangements would that be? The cost will be $_____ if Mrs. Coleman orders _____ of the small arrangements.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Mrs. Coleman is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Norwood Florist charges $16 for each smaller arrangement, plus  $33 for the large centerpiece. Adam's Flowers, in contrast, charges $41 for the large centerpiece and $8 per arrangement for the rest. If Mrs. Coleman orders a certain number of small arrangements, the cost will be the same at either flower shop. What would the total cost be? How many small arrangements would that be?   The cost will be $_____ if Mrs. Coleman orders _____ of the small arrangements.

Bytelearn · Accepted Answer

Define Costs and Variables: Let's denote the cost of the large centerpiece from Norwood Florist as N and from Adam's Flowers as A. Let's denote the cost per smaller arrangement from Norwood Florist as n and from Adam's Flowers as a. Let's denote the number of small arrangements as x. We are given that N = $33, n = $16, A = $41, and a = $8. We need to find the total cost and the number of small arrangements (x) for which the cost is the same at both flower shops.Norwood's Total Cost Equation: Write the equation for the total cost at Norwood Florist, which is the cost of the large centerpiece plus the cost of x small arrangements. Norwood's total cost equation: 33 + 16xAdam's Total Cost Equation: Write the equation for the total cost at Adam's Flowers, which is the cost of the large centerpiece plus the cost of x small arrangements. Adam's total cost equation: 41 + 8xSet Equations Equal: Since the total cost is the same at both flower shops, we can set the two equations equal to each other to find the value of x. 33 + 16x = 41 + 8xSolve for x: Solve for x by subtracting 8x from both sides of the equation. 33 + 16x - 8x = 41 + 8x - 8x 33 + 8x = 41Isolate Variable x: Subtract 33 from both sides of the equation to isolate the variable x. 33 + 8x - 33 = 41 - 33 8x = 8Calculate Total Cost: Divide both sides of the equation by 8 to solve for x. 8x / 8 = 8 / 8 x = 1Now that we have the number of small arrangements (x), we can calculate the total cost by substituting x back into either of the total cost equations. We'll use Norwood's equation for this calculation. Total cost = 33 + 16(1) Total cost = 33 + 16 Total cost = 49

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