Question

Logical Reasoning Describe the pattern shown in the table. Then write a variable expression involving n to complete the table. In the table, the three dots indicate that the pattern continues.

Short answer

The complete table is:

Cost of item (dollars)	1.00	2.00	3.00	4.00	…	$\$n$
Cost of tax (dollars)	1.05	2.10	3.15	4.20	…	$1.05n$

Step-by-step solution

Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given

Consider, the table provided in the question,

Cost of item (dollars)	1.00	2.00	3.00	4.00	…	n
Cost of tax (dollars)	1.05	2.10	3.15	4.20	…	?

Step-3 – Complete the table

From the table provided in the question, it can be observed that the cost of each item is $1 and tax on each item is $0.05.

Hence, the variable expression for Cost of n items is $\$n$.

The variable expression for Cost with tax of n items is obtained as:

$\begin{array}{l}\$\left(n+0.05n\right)\\ =n\left(1+1.05\right)\\ =1.05n\end{array}$

The complete table is shown below:

Cost of item (dollars)	1.00	2.00	3.00	4.00	…	$\$n$
Cost of tax (dollars)	1.05	2.10	3.15	4.20	…	$1.05n$