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 wants the words to all be horizontal in the final mosaic. the word tiles come in two 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?

Calculate the cost per square foot for each size tile.

1 square foot = 144 square inches.

Small tile = 4 x 4 = 16 square inches.

16 / 144 = 1/9 square foot.

Cost per square foot = 3.50 / 1/9 = $31.50 per square foot.

Large tile = 6 x 12 = 72 square inches.

72 / 144 = 1/2 square foot.

Cost per square foot = 4.50 / 1/2 = $9 per square foot.

The minimum area of the mosaic is 3 feet x 5 feet = 15 square feet.

The large tiles are cheaper per square foot.

Total tiles needed = 15 sq. ft.  / 1/2 sq. ft = 30 tiles.

30 tiles x 4.50 each = $135

your answer would be 10x - 1

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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