[Video] Q35: C(x) = mx + 500a company's total cost c(x), in dollars, to produce x shirts is given by the function above, where m is a constant and x > 0. the total cost to produce 100 shirts is $800. what is the total cost, in dollars, to produce 1000 shirts? (disregard the $ sign when gridding your answer.)

Explanation for Question 35 From the Math (Calc) Section on the 2019 October Sat

Not for number 35. We're given this equation right here where C of X 2 is our cost for the company. And X is the number of shirts. 3 And we're asked to find the costs, which is C of X when we 4 have to print 1000 shirts. So let's start by plugging in what we know, 5 right. CFX is what we're solving for. We don't know what M is. 6 We know the X must be 1000 and then we're going to add 500 7 to that. And so here, you kind of have to stop in your tracks, 8 right? Because we don't know what M is. So there's no way for us 9 to solve for C of X, since we only have one equation, 10 but two unknown variables. However, 11 we can use information from earlier in the question to solve for M and 12 that's going to be right here where the total cost to produce 100 shirts 13 is $800, right? 14 Because if the cost is $800 and we have 100 15 shirts, right? So 100 times M plus 500 with that 16 information, we can now solve for N and then plug that in to our 17 equation up here. That way we can now solve for the cost, 18 right? So let's solve for M we'll start by subtracting 500 from both sides. 19 These five hundreds will cancel leaving us with a 300 is equal to 100 20 M and then we simply need to divide by a hundred. 21 That way these one hundreds will cancel leaving us with just M as equal 22 to three. And now that we know the M is equal to three, 23 we can go back up to this topic equation, 24 which is the Walmart actually interested in with the 1000 and replace our M 25 with the three, because now we know the value three times, 26 1000 that's 3000. We're going to add 500 to that at 3000 27 plus 500 gives us our answer of 3,500.