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

The pattern for hats is
`(n)/(1.5)` and the pattern for scarves is
`n* 1.5` ; where n is the no. of hat or scarf respectively

Step-by-step explanation:

Let, cost of hat and scarves be x and y respectively

Then, according to question,

y (cost of scarves) =
`1.5 *  x` (cost of hats)

or,
`x =(y)/(1.5)`

Calculating for hats,

For 1 hat; putting y = 1
`x = (1)/(1.5)`

For 2 hats; putting y = 2
`x = (2)/(1.5)`

For 3 hats; putting y = 3
`x = (3)/(1.5)`

For 4 hats; putting y = 4
`x = (4)/(1.5)`

For 5 hats; putting y = 5
`x = (5)/(1.5)`

Therefore, we can see the pattern for hats is
`(n)/(1.5)`, where n is no. of hats

Calculating for scarves,

For 1 scarves; putting x = 1 x =
`1* 1.5`= 1.5

For 2 scarves; putting x = 2 x =
`2* 1.5`= = 3.0

For 3 scarves; putting x = 3 x =
`3* 1.5`= = 4.5

For 4 scarves; putting x = 4 x =
`4* 1.5`= = 6.0

For 5 scarves; putting x = 5 x =
`5* 1.5`= = 7.5

Therefore, we can see the pattern for scarves is
`n* 1.5`, where n is no. of scarves