Question

) For each problem, select the variable inequality that describes the problem situation and select the variable to represent the unknown quantity. (See the question in the problem.) Jarrell deposits $225 each month into his bank account for a new soundboard that costs at least $3,500. If the bank withdraws $120 from his account for fees, for how many months will Jarrell need to save to be able to buy the soundboard?

Answer 1

Jarrell needs to save for at least 34 months to buy a soundboard costing at least $3,500, given he saves $225 each month but the bank withdraws $120 for fees, leaving an effective monthly saving of $105.

Step-by-step explanation:

To determine for how many months Jarrell will need to save to buy a soundboard, let's define the variable m to represent the total number of months needed.

The cost of the soundboard is at least $3,500, and Jarrell deposits $225 each month, but since the bank withdraws $120 for fees each time a deposit is made, the effective monthly saving amount is $225 - $120 = $105.

So the inequality to describe the savings over m months would be: 105m ≥ 3500. To solve for m, divide both sides of the inequality by 105: ≥ 3500 / 105

Now m is calculated as ≥ 33.333...

Since we can't have a fraction of a month, we round up to the next whole number, so Jarrell will need to save for at least 34 months to buy the soundboard.