Mrs. Espinoza 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. Silvergrove Florist charges $8 for each smaller arrangement, plus $32 for the large centerpiece. Sadie's Flowers, in contrast, charges $50 for the large centerpiece and $7 per arrangement for the rest. If Mrs. Espinoza 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?
Question
Mrs. Espinoza 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. Silvergrove Florist charges 32 for the large centerpiece. Sadie's Flowers, in contrast, charges 7 per arrangement for the rest. If Mrs. Espinoza 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?
Solution
To solve this problem, we need to set up an equation where the cost of the flower arrangements from Silvergrove Florist equals the cost from Sadie's Flowers.
Let's denote the number of smaller arrangements as x.
The cost at Silvergrove Florist is 32 for the large centerpiece, so the total cost is 8x + 32.
The cost at Sadie's Flowers is 50 for the large centerpiece, so the total cost is 7x + 50.
Setting these two equations equal to each other gives us:
8x + 32 = 7x + 50
Solving for x, we subtract 7x from both sides to get:
x = 50 - 32 = 18
So, Mrs. Espinoza would need to order 18 small arrangements for the cost to be the same at both flower shops.
To find the total cost, we can substitute x = 18 into either of the original equations. Let's use the first one:
Total cost = 8*18 + 32 = $176
So, the total cost would be $176 for 18 small arrangements and one large centerpiece.
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