Question

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 1

Answer:

The pattern for hats is $\frac{n}{1.5}$ and the pattern for scarves is $n\times 1.5$ ; 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) = $1.5 \times x$ (cost of hats)

or,$x =\frac{y}{1.5}$

Calculating for hats,

For 1 hat; putting y = 1         $x = \frac{1}{1.5}$

For 2 hats; putting y = 2   $x = \frac{2}{1.5}$

For 3 hats; putting y = 3   $x = \frac{3}{1.5}$

For 4 hats; putting y = 4           $x = \frac{4}{1.5}$

For 5 hats; putting y = 5   $x = \frac{5}{1.5}$

Therefore, we can see the pattern for hats is $\frac{n}{1.5}$, where n is no. of hats

Calculating for scarves,

For 1 scarves; putting x = 1   x = $1\times 1.5$= 1.5

For 2 scarves; putting x = 2   x = $2\times 1.5$= = 3.0

For 3 scarves; putting x = 3   x = $3\times 1.5$= = 4.5

For 4 scarves; putting x = 4   x = $4\times 1.5$= = 6.0

For 5 scarves; putting x = 5   x = $5\times 1.5$= = 7.5

Therefore, we can see the pattern for scarves is$n\times 1.5$, where n is no. of scarves