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

Answer:

Expression is : $Tax=\frac{6.5}{100}(12x+10)$

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

Step-by-step 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:

$Tax=6.5\%\times C\\Tax=\frac{6.5}{100}(12x+10)$

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

$Tax=\frac{6.5\times 12x}{100}+\frac{6.5\times 10}{100}\\\\Tax=\frac{78x}{100}+\frac{65}{100}\\\\Tax=0.78x+0.65$

Therefore, the simplified expression is:

$Tax=0.78x+0.65$