Question

Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part III: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same amount in fees?

Part IV: How many checks would Cecily need to write per month for the accounts to charge the same amount in fees?​

Answer 1

Part 3

Checking account A has a monthly fee of $16 and a per-check fee of $0.08

If she writes x checks, where x is some nonnegative whole number, then she is charged an additional 0.08x dollars on top of the 16 dollar fee.

The total cost of checking account A is 0.08x+16 dollars.

The total cost of account B is 0.12x dollars for similar reasoning. We don't have a monthly fee, but the cost per check is higher.

Set the two expressions equal to one another to get your answer.

Answer:  0.08x+16 = 0.12x

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Part 4

Let's solve the equation we set up in part 3

0.08x+16 = 0.12x

16 = 0.12x-0.08x

16 = 0.04x

0.04x = 16

x = 16/0.04

x = 400

If Cecily wrote 400 checks per month, then the cost of each account would be the same.

For account A, it would cost her 0.08*x+16 = 0.08*400+16 = 48 dollars

For account B, it would cost her 0.12*x = 0.12*400 = 48 dollars.

Answer: 400 checks per month