Lydia is comparing two checking accounts one has a monthly fee of $10 and a per check fee of $0.10 and the other has a monthly fee of $5 and a per check of $0.25. what is the minimum number of checks lydia needs to write for the first bank to be a better option

Hi there! So to solve these kinds of questions, let's smash the two situations together into equations. When you do this, you would get this: 10 + 0.10x = 5 + 0.25x. This is because the monthly fees are the one-time price and the per check fee is based on how many checks are cashed. First, let's subtract the 0.25x from both sides to get the whole number on the right side by itself. When you do that, you get 10 - 0.15x = 5. Now, subtract each side by 10 to get the other number with the variable by itself. When you do, you get -0.15x = -5. Now, divide each side by -0.15 to isolate the variable. -5/-0.15 is 33.333 or 33 when rounded to the nearest whole number. Test out the solutions and you get that 13.3 > 13.25. 33 checks is not enough. But when we add another check you get 13.4 < 13.5. For the first bank to be the best option, Lydia would need to write at least 34 checks.