Chapter 1.1, Problem 47E

a.

To determine

To write: and solve equation to find amount spent on each CD.

Answer to Problem 47E

  $\$7.60$

Explanation of Solution

Given:

Amount spent on 4 CD’s is $30.40.

Each CD costs the same and is on sale for 80% of original price.

Let the cost of 1 CD due to sale be $ x .

Now,

Number of CD’s $\times$ Amount spent on each CD = Total amount spent

Thus,

  $\begin{array}{c}4x=30.40\\ x=\frac{30.40}{4}\\ x=7.6\end{array}$

Conclusion:

Thus, the amount spent on each CD is $7.6.

b.

To determine

To explain: is it possible to buy 3 CD’s if you have $ 25 and CD’s are no more on sale.

Answer to Problem 47E

No

Explanation of Solution

Given:

CD is on sale for 80% of original price.

From part (a), the amount spent on each CD is $7.6.

Let the original price of the CD be $ x.

Amount spent on each CD = 80% $\times$ original price

That is,

  $\begin{array}{c}\text{7}\text{.6}=0.80\times x\\ 7.6=0.8x\\ \frac{7.6}{8}=x\\ 9.5=x\end{array}$

Then, the cost of 3 such CD’s is:

Number of CD’s $\times$ Amount spent on each CD = Total amount spent

Thus,

  $\begin{array}{c}\text{Amount spent on buying 3 CD's}=3\left(9.5\right)\\ =\frac{30.40}{4}\\ =\$28.50\end{array}$

Conclusion:

The original price of 3 CD’s is $28.50, so $25 is not enough to buy them.