Question

16. You must maintain a minimum balance of $50 in your checking account. You currently have a balance of $280. a. Write and solve an inequality that represents how many $20 bills you can withdraw from the account without going below the minimum balance.b. Your bank charges an ATM fee of $2.50, which is charged each time you withdraw $20. Write and solve an inequality that represents how many $20 bills you can withdraw from the account without going below the minimum balance in this situation.

Answer 1

a.

`280 - n*20\geq50\\n\leq11`

b.

`280 - n*(20+2.50)\geq 50\\n\leq10`

Step-by-step explanation:

a. For the first situation, the goal is to make sure that a minimum amount of $50 (balance ≥ 50) is left on the account after withdrawing "n" $20 bills from an initial $280 (balance = 280 - 20n). The inequality can be modeled and solved as follows:

`280 - n*20\geq50\\n\leq(280-50)/(20) \\n\leq11.5`

Since the problem deals with $20 bills, only whole quantities should be considered and then, the inequality should be written as:

`n\leq11`

b. This situation is very similar to the previous one but it has an additional $2.50 fee for each $20 bill withdrawn (balance = 280 - n(20+2.50)). The inequality can be modeled as follows

`280 - n*(20+2.50)\geq 50\\n\leq(280-50)/(22.5)\\n\leq10.22`

Once again, only whole quantities are considered, so the inequality yields:

`n\leq10`