Chapter 1.2, Problem 28E

To determine

and explain whether shehas enough money for all the items she purchased.

Answer to Problem 28E

Yes she has enough money. She has $\$100$ and she spent $\$93.01$ on purchasing three items.

Explanation of Solution

Given information: The original prices for items are as follows:

  $\begin{array}{l}\text{Sweater}=\$43.98\\ Pair\text{ of Jeans}=\$38.59\\ \text{Blouse}=\$31.99\end{array}$

  $\begin{array}{l}\text{Discount on original price}=25\%\\ \text{Tax= 8}\text{.25\%}\\ \text{Money that Sara has}=\$100\end{array}$

Calculation:

Total original price of the items (i.e. sweater, jeans and blouse) can be calculated as follows:

  $\begin{array}{c}\text{Total price = }\$43.98+\$38.59+\$31.99\\ =\$114.56\end{array}$

Since the discount on all the three items is same i.e 25%.

So the total discount will be $=3\times 25\%=75\%$

Now, the subtotal with discount can be evaluated as follows:

  $\begin{array}{c}\text{Subtotal with discount}=\left(\text{Total price}\right)\left(\text{Discount percent}\right)\\ =\left(\$114.56\right)\left(75\%\right)\\ =\left(\$114.56\right)\left(\frac{75}{100}\right)\\ =\$85.92\end{array}$

Now, the tax to be paid on three items will be calculated as follows:

  $\begin{array}{c}\text{Amount of tax}=\left(\text{Subtotal with discount}\right)\left(\text{Tax percent}\right)\\ =\left(\$85.92\right)\left(8.25\%\right)\\ =\left(\$85.92\right)\left(\frac{8.25}{100}\right)\\ =\$7.09\end{array}$

The total amount paid by Sara for the purchase of three items can be calculated as follows:

  $\begin{array}{c}\text{Grandtotal}=\left(\text{Subtotal with discount}\right)+\left(\text{Tax percent}\right)\\ =\left(\$85.92\right)+\left(\$7.09\right)\\ =\$93.01\end{array}$

The total amount paid by Sara is $\$93.01$ , that is less than the total amount she has, i.e. $\$100$ .