Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mrs. Moore 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. Bloomington Florist charges $10 for each smaller arrangement, plus $45 for the large centerpiece. Quincy's Flowers, in contrast, charges $47 for the large centerpiece and $9 per arrangement for the rest. If Mrs. Moore orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be? If Mrs. Moore orders _____ small arrangements, it will cost $_____ at either shop.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Mrs. Moore 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. Bloomington Florist charges $10 for each smaller arrangement, plus  $45 for the large centerpiece. Quincy's Flowers, in contrast, charges $47 for the large centerpiece and $9 per arrangement for the rest. If Mrs. Moore orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?   If Mrs. Moore orders _____ small arrangements, it will cost $_____ at either shop.

Bytelearn · Accepted Answer

Set up equations: Set up the equations based on the given information. Bloomington Florist: Cost = $10 per small arrangement + $45 for large centerpiece. Quincy's Flowers: Cost = $9 per small arrangement + $47 for large centerpiece. Let x be the number of small arrangements and C be the total cost at either shop. Equation for Bloomington Florist: 10x + 45 = C Equation for Quincy's Flowers: 9x + 47 = CEqualize equations: Since the costs are the same, we can set the two equations equal to each other to find the number of small arrangements. 10x + 45 = 9x + 47Solve for x: Solve for x by subtracting 9x from both sides of the equation. 10x - 9x + 45 = 9x - 9x + 47 x + 45 = 47Substitute x: Subtract 45 from both sides to solve for x. x + 45 - 45 = 47 - 45 x = 2Find total cost: Now that we have the number of small arrangements, we can find the total cost by substituting x back into either original equation. Using Bloomington Florist's equation: 10x + 45 = C 10(2) + 45 = C 20 + 45 = C C = 65Verify solution: Verify the solution by substituting x into Quincy's Flowers' equation. 9x + 47 = C 9(2) + 47 = C 18 + 47 = C C = 65

Full solution

More problems from Solve a system of equations using any method: word problems

Related topics