Question

You want to determine the savings for using a battery that can be recharged. The battery costs sixteen dollars. You save four dollars each time you recharge the battery. Represent the cost of the rechargeable battery as a negative number and savings as a positive number.

Define a unit for the net savings of the rechargeable battery.
What is your net savings if you recharge the battery ten times?
If your net savings is twelve dollars, how many times did you recharge the battery?
Complete the rows for the amount you save each time you recharge the battery and the cost of a rechargeable battery. Then, enter a variable for the number of rechargings and use this variable to write an expression for the net savings of the rechargeable battery.

Answer 1

- The cost of the rechargeable battery is -$16 (negative because it is a cost).
- The savings each time you recharge the battery is $4 (positive because it is a savings).

We can define the unit for net savings as dollars per recharge.

If you recharge the battery ten times, your net savings would be:

Net savings = (Savings per recharge x Number of recharges) - Cost of battery
Net savings = ($4 x 10) - $16
Net savings = $40 - $16
Net savings = $24

Therefore, your net savings would be $24 if you recharge the battery ten times.

If your net savings is $12, we can use the same formula to find the number of times you recharged the battery:

Net savings = (Savings per recharge x Number of recharges) - Cost of battery
$12 = ($4 x n) - $16
$12 + $16 = $4n
$28 = $4n
n = 7

Therefore, you would have recharged the battery 7 times if your net savings is $12.

The table for the cost of the rechargeable battery and savings each time you recharge the battery is:

| Rechargeable battery cost | Savings per recharge |
|---------------------------|----------------------|
| -$16 | $4 |

Using the variable r to represent the number of recharges, we can write an expression for the net savings of the rechargeable battery as:

Net savings = (Savings per recharge x Number of recharges) - Cost of battery
Net savings = ($4r) - (-$16)
Net savings = $4r + $16

Therefore, the expression for the net savings of the rechargeable battery in terms of the number of recharges is $4r + $16.