An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist ants the words to all be horizontal in the final mosaic. The word tiles come in to sizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?

Question

An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist ants the words to all be horizontal in the final mosaic. The word tiles come in to sizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?

Answer 1

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Answer 2

my teacher said answer is not correct correct answer is 6 tiles and cost is$27

Answer 3

To find the minimum cost and the number of each tile needed to minimize the cost, we will need to determine the number of small tiles and large tiles that can fit within the given space.

Given:
- Space allocated: 4 feet tall and 6 feet wide
- Mosaic size requirement: at least 3 feet tall and 5 feet wide
- Small tiles size: 4 inches tall and 4 inches wide
- Large tiles size: 6 inches tall and 12 inches wide
- Cost of small tiles: $3.50 each
- Cost of large tiles: $4.50 each

First, we need to convert the dimensions from feet to inches:
- Space allocated: 4 feet tall x 6 feet wide = 48 inches tall x 72 inches wide
- Mosaic size requirement: at least 3 feet tall and 5 feet wide = at least 36 inches tall and 60 inches wide

Now, let's calculate the number of small tiles and large tiles that fit within the given space.

For the height:
- Number of small tiles that fit vertically: 48 inches / 4 inches = 12 small tiles
- Number of large tiles that fit vertically: 48 inches / 6 inches = 8 large tiles

For the width:
- Number of small tiles that fit horizontally: 72 inches / 4 inches = 18 small tiles
- Number of large tiles that fit horizontally: 72 inches / 12 inches = 6 large tiles

As we want to use the fewest tiles to minimize the cost, we need to use the larger tiles whenever possible.

Since the mosaic must be at least 36 inches tall and 60 inches wide, we can only fit 1 row of large tiles vertically and 5 rows of large tiles horizontally.

Calculating the total number of each tile required:
- Number of small tiles needed: 18 horizontal x 5 vertical = 90 small tiles
- Number of large tiles needed: 6 horizontal x 1 vertical = 6 large tiles

Now, let's calculate the cost:
- Cost of small tiles: $3.50 x 90 = $315
- Cost of large tiles: $4.50 x 6 = $27

The minimum cost is the sum of the costs of small and large tiles:
- Minimum cost = $315 + $27 = $342

Therefore, to minimize the cost, the artist should use 90 small tiles and 6 large tiles, resulting in a minimum cost of $342.