Chapter 1.2, Problem 48STP

(a)

To determine

To complete: the given table

Answer to Problem 48STP

Number of days	Expression evaluation	Total cost ($)
2	$2\times 2+3\times 2=4+6=10$	10
4	$4\times 2+3\times 4=8+12=20$	20
6	$6\times 2+3\times 6=12+18=30$	30

Explanation of Solution

Given:

DVDs cost $4 to rent for two days

Games cost $3 to rent for one day

Number of Days	Total Cost ($)
2	¦
4	¦
6	¦

Calculation:

Let one DVD is rented for x days (since, rent of DVD is fixed for 2 days, thus x should be a multiple of two as otherwise also rent will be calculated on the next multiple of 2 that comes after x)

Let one game is rented for y days.

Then cost of renting one DVD for x days $=4\times \frac{x}{2}=2x$

Cost of renting one game for y days $=3y$

Then total cost $2x+3y$

To complete the table, we take $x=y=$ number of days given in table for each row.

Number of days	Expression evaluation	Total cost ($)
2	$2\times 2+3\times 2=4+6=10$	10
4	$4\times 2+3\times 4=8+12=20$	20
6	$6\times 2+3\times 6=12+18=30$	30

Conclusion:

Thus, the given table is completed.

(b)

To determine

To find: the total cost of buying 4 DVD's and 3 games for 10 days

Answer to Problem 48STP

The total cost of buying 4 DVD's and 3 games for 10 days is $170

Explanation of Solution

Calculation:

Since, cost of renting one DVD for x days $=2x$

Therefore, cost of renting 4 DVD's for x days $=4\times 2x=8x$

Since, cost of renting one game for y days $=3y$

Therefore, cost of renting three games for y days $=3\times 3y=9y$

Hence, the total cost $=8x+9y$

Now, substituting, $x=y=10$

  $\begin{array}{l}8x+9y=8\times 10+9\times 10\\ =80+90\\ =\$170\end{array}$

Thus, the total cost of buying 4 DVD's and 3 games for 10 days is $170

Conclusion:

Thus, the total cost of buying 4 DVD's and 3 games for 10 days is $170