Mrs. Tyler 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. Dayton Florist charges $12 for each smaller arrangement, plus $40 for the large centerpiece. Grace's Flowers, in contrast, charges $50 for the large centerpiece and $10 per arrangement for the rest. If Mrs. Tyler orders a certain number of small arrangements, the cost will be the same at either flower shop. What would the total cost be? Write a system of equations, graph them, and type the solution. ____ dollars

Question

Mrs. Tyler 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. Dayton Florist charges $12 for each smaller arrangement, plus  $40 for the large centerpiece. Grace's Flowers, in contrast, charges $50 for the large centerpiece and $10 per arrangement for the rest. If Mrs. Tyler orders a certain number of small arrangements, the cost will be the same at either flower shop. What would the total cost be?  Write a system of equations, graph them, and type the solution.  ____ dollars

Bytelearn · Accepted Answer

Define x and write cost equations:  Let x be the number of smaller arrangements Mrs. Tyler orders. Write the cost equations for both florists. Dayton Florist: Total cost = $12x + $40. Grace's Flowers: Total cost = $10x + $50. Set equations equal to find x:  Set the equations equal to each other to find the number of arrangements where the costs are the same. $12x + $40 = $10x + $50. Solve for x:  Solve for x by subtracting $10x from both sides: $2x + $40 = $50. Substitute x back in equation:  Subtract $40 from both sides: $2x = $10. Calculate total cost:  Divide both sides by 2 to find x: x = 5. This means Mrs. Tyler needs to order 5 smaller arrangements for the costs to be the same at both florists.  Substitute x = 5 back into either original cost equation to find the total cost. Using Dayton's equation: Total cost = $12(5) + $40 = $60 + $40 = $100.

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