Question

Ray wants to buy a hat that costs $10 and some shirts that cost $12 each.

The sales tax rate is 6.5%, Write an expression to determine the amount
of sales tax that Ray will pay on his entire purchase. Expand to simplify
the expression

Answer 1

Expression is :
`Tax=(6.5)/(100)(12x+10)`

Simplified expression is :
`Tax=0.78x+0.65`

Explanation:

Let the number of shirts bought be 'x'.

Given:

Number of hats bought = 1

Number of shirts bought = 'x'

Cost of 1 hat = $10

Cost of 1 shirt = $12

Sales tax percent = 6.5%

Since, cost of 1 shirt is $12.

Therefore, cost of 'x' shirts is =
`12x`

Now, total cost of 'x' shirts and 1 hat is the sum of both the costs. Thus,

Total cost is,
`C=12x+10`

Now, sales tax applies on total cost. So, sales tax is given as:

`Tax=6.5\%* C\\Tax=(6.5)/(100)(12x+10)`

Now, expanding the above expression to simplify further by using the distributive property of addition, we get:

`Tax=(6.5* 12x)/(100)+(6.5* 10)/(100)\\\\Tax=(78x)/(100)+(65)/(100)\\\\Tax=0.78x+0.65`

Therefore, the simplified expression is:

`Tax=0.78x+0.65`