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

Answer:

a.

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

b.

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

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:

$280 - n*20\geq50\\n\leq\frac{280-50}{20} \\n\leq11.5$

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b. This situation is very similar to the previous one but it has an additional $2.50 fee for each $20 bill withdrawn (balance = 280 - n(20+2.50)).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

$280 - n*(20+2.50)\geq 50\\n\leq\frac{280-50}{22.5}\\n\leq10.22$

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

$n\leq10$