Two-step equation word problem: computers

marsha has just opened her new computer store she makes $27 on every computer she sells and her monthly expenses are $10,000 what is the minimum number of computer she used to sell in a month to make a profit so I'll let you think about that for a second well let's think what we have to figure out we have to figure out the number the minimum number of computer she needs to sell so let's set that to a variable or set a variable to represent that so let's let X equal the number of computer she sells number of computers computers sold now let's think about how much net profit she will make in a month and that's what we're thinking about how many how many computers the minimum number she's to sell in order to make a net profit so I'll write her profit her profit is going to be how much money she brings in from selling in selling the computers and she makes $27 on every computer she sells so her profit is going to be $27 times the number of computer she sells she has $27 per computer times the number she sells but we're not done yet she still has expenses of $10,000 per month so we're gonna have to subtract out we're gonna have to subtract out the $10,000 what we care about is making a profit we want this number right over here to be greater than 0 so let's just think about what number of computers would get us to 0 and then she if maybe she's just a little bit more than that so let's say let's see what gets her to break-even so break even that's zero profit neither positive or negative is equal to 27 times and I'll do it all in one color now 27 X minus 10,000 well we've seen equations like this before we can add 10,000 to both sides add 10,000 to both sides so that it gets so it's no longer on the right-hand side and we are left with we are left with 10,000 10,000 is equal to 20 is equal to 27 X and then to solve for X we just have to divide both sides by 27 let's do that divide both sides by 27 on our right hand side we have X so let me just write this down so we have X on our right hand side is going to be equal to 10,000 over 27 it is going to be equal to 10,000 over 27 I switched the right and the left hand sides here now what is this going to be well we can do a little bit of long division to handle that so 27 goes into 10,000 so 27 doesn't go into one doesn't go into 10 it goes into 103 times 3 times 27 is what 81 81 100 minus 81 is 19 then we can bring down 0 27 goes into 190 it looks like it'll go into it about 6 times let's see if that's right 6 times 7 is 42 6 times 2 is 12 plus 4 16 let's see 90 minus 62 is actually 20 28 oh yeah so let me let me turn this back so go 7 times 7 times 7 is 49 7 times 2 is 14 plus 4 is 18 there you go look at that so 190 minus 189 we get 1 let's bring down another 0 we bring down C we bring down another 0 we have a 0 right there 27 goes into 10 how many times well doesn't go into 10 at all put a 0 right there 0 times 27 is 0 that we subtract and then we get 10 again and now we're in the decimal range or we're going to start getting decimal values but we could bring out another 0 we could get 27 goes into 100 3 times so our x value is going to be approximately 370 point 3 and then we're going to keep going on and on and on and on but this is enough information for us to answer our question what is the minimum number of computer she needs to sell in a month to make a profit well she can't sell a decimal number of computers 1/3 of a computer she could either sell 300 many computers if she sells 370 computers that she's not going to get to break even because that's less than the quantity she needs for break even so she needs to sell 371 she needs to sell 371 computers in a month to make a profit