a shop sells hats and scarves.The scarves cost 1.5 times as much as the hats.Writ 2 patterns that could represent the costs of 1,2,3,4 and 5 hats and scarves. List the 5 terms of each pattern.Then explain how to find the cost of 6 hats and scarves using the the pattern you wrote.

Answer: The pattern for hats is [tex]\frac{n}{1.5}[/tex] and the pattern for scarves is [tex]n\times 1.5[/tex] ; where n is the no. of hat or scarf respectively Explanation: Let, cost of hat and scarves be x and y respectively Then, according to question, y (cost of scarves) = [tex]1.5 \times  x[/tex] (cost of hats) or,[tex]x =\frac{y}{1.5}[/tex]Calculating for hats, For 1 hat; putting y = 1         [tex]x = \frac{1}{1.5}[/tex]For 2 hats; putting y = 2   [tex]x = \frac{2}{1.5}[/tex]For 3 hats; putting y = 3   [tex]x = \frac{3}{1.5}[/tex]For 4 hats; putting y = 4           [tex]x = \frac{4}{1.5}[/tex]For 5 hats; putting y = 5   [tex]x = \frac{5}{1.5}[/tex]Therefore, we can see the pattern for hats is [tex]\frac{n}{1.5}[/tex], where n is no. of hats Calculating for scarves, For 1 scarves; putting x = 1   x = [tex]1\times 1.5[/tex]= 1.5 For 2 scarves; putting x = 2   x = [tex]2\times 1.5[/tex]= = 3.0 For 3 scarves; putting x = 3   x = [tex]3\times 1.5[/tex]= = 4.5 For 4 scarves; putting x = 4   x = [tex]4\times 1.5[/tex]= = 6.0 For 5 scarves; putting x = 5   x = [tex]5\times 1.5[/tex]= = 7.5 Therefore, we can see the pattern for scarves is[tex]n\times 1.5[/tex], where n is no. of scarves