Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Mrs. Kerr 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. Lakeside Florist charges $13 for each smaller arrangement, plus $44 for the large centerpiece. Emily's Flowers, in contrast, charges $40 for the large centerpiece and $17 per arrangement for the rest. If Mrs. Kerr 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. Kerr orders _____ of the small arrangements.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Mrs. Kerr 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. Lakeside Florist charges $13 for each smaller arrangement, plus  $44 for the large centerpiece. Emily's Flowers, in contrast, charges $40 for the large centerpiece and $17 per arrangement for the rest. If Mrs. Kerr 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. Kerr orders _____ of the small arrangements.

Bytelearn · Accepted Answer

Define Variables: Let x represent the number of small arrangements Mrs. Kerr orders. The total cost at Lakeside Florist would be the cost of the large centerpiece plus the cost of x small arrangements. Therefore, the equation for Lakeside Florist is: Cost = $44 (large centerpiece) + $13x (small arrangements) Cost = 44 + 13xEquation for Lakeside Florist: Similarly, the total cost at Emily's Flowers would be the cost of the large centerpiece plus the cost of x small arrangements. The equation for Emily's Flowers is: Cost = $40 (large centerpiece) + $17x (small arrangements) Cost = 40 + 17xEquation for Emily's Flowers: Since the cost will be the same at either flower shop when Mrs. Kerr orders a certain number of small arrangements, we can set the two equations equal to each other to find the value of x: 44 + 13x = 40 + 17xSet Equations Equal: Now we solve for x by subtracting 13x from both sides of the equation: 44 + 13x - 13x = 40 + 17x - 13x 44 = 40 + 4xSolve for x: Next, we subtract 40 from both sides of the equation to isolate the term with x: 44 - 40 = 40 + 4x - 40 4 = 4xIsolate x Term: Finally, we divide both sides by 4 to solve for x: 4 / 4 = 4x / 4 1 = xFinal Solution: Now that we know x = 1, we can find the total cost by substituting x back into either of the original equations. We'll use the Lakeside Florist equation: Cost = 44 + 13x Cost = 44 + 13(1) Cost = 44 + 13 Cost = 57

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