Ingrid makes quilts in designs that follow a specific pattern. The first three designs are shown. In designs, the white blocks r

Question

2 years ago

10

epresent blocks containing pictures while the gray blocks represent border blocks of a single color.

1 answer:

Gekata [30.6K] · Answer 1 · 2023-05-26T07:29:20+03:00

The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt

The numbers and patterns of the blocks are;

a. Patterns;

The height of the white blocks is the Design number, while the rows are one more than the design number

The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number

b. The function is $\underline{p(n) = n \cdot (n + 1)}$

c. The function is $\underline{b(n) = (n + 2) \cdot (n + 3) - n \cdot (n + 1)}}$

d. $\underline{t(n) = (n + 2) \cdot (n + 3) = b(n) - p(n) }$

e. The design chosen is Design 9

The number of blocks is 132 blocks

Reasons:

The pattern of the design are;

a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks

Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks

The number of white blocks in a design, n is the product of n and (n + 1)

The number of grey blocks in a design n, is the product of (n + 2) and (n + 3) less the number of white blocks in the design

b. Based on the above, the function that represent the number of picture blocks in Design n, is therefore;

c. Based on the above, the function that represent the number of border blocks in Design n, is therefore;

d. The total number of blocks, t(n) = (n + 2)·(n + 3)

t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)

e. The given number of picture blocks = 90

The number of picture blocks in a design, n = n × (n + 1)

Therefore, given that the number of picture blocks is 90, we have;

90 = n × (n + 1)

n² + n - 90 = 0

(n + 10)·(n - 9) = 0

n = 9, or n = -10

Therefore, the design museum chooses is Design 9

The total number of blocks in a quilt design, t(n) = (n + 2)·(n + 3)

Total blocks in the design the art museum choses, t(9), is given as follows;

t(9) = (9 + 2)·(9 + 3) = 132 blocks

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