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Bonus Car Rental charges $\$ 39.95$ per day plus $\$ 0.10$ per mile to rent a midsize car. Jonas spent $\$ 54.75$ on a 1 -day rental. How far did he drive the car?

Oh, okay, So this swan auto rental charges $32 per day, So I'm gonna put D for day plus 0.18 miles for an automobile automobile rental. Okay, so a layover here. So part, eh? Elaine over here rented a car for one day and drove 60 83 miles. Drove anything Miles. OK, how much did you pay? So we'll just plug it into that equation. So one is equal to D 83 is equal to m. So then you do 32 times one plus 0.18 times 83. Okay, pull up a calculator. So 0.18 times 83 this 14.94 And I add that to 32. That's going to get me 46.94 dollars. So this is part of a Okay, So parts be Ramon. He paid $69.80 for one day. How far do you drive? So his total. So this whole equation is equal to the total. So his total was 69.80 and he drove for one day. So D is one. We're trying to figure out how many miles he drove. So we're like honey Wiles. So then just solve for him. So then isolate the variable. So subtract 32 3 Churchills wanted just 32. Okay, so 69.80. Rinus 32 ISS 37.8 is equal to 0.18 AM. Okay. Oh, 37 points. Eight divided by isolate the end. So divide by 0.18 Okay, so you get M is equal to 210 So if you drove 210 miles and that is your answer for a party

Problem 26 The customer mile of operating court is a function of its speed. We know that if the speed is 10 MPH, the cost is 28 and if it's 30 cost is 22. And finally, if the speed is 50 MPH, the cost is 24. We want to find see as a function of the which means we want to get he B and C to do so we want three equations and we can get the three equations from these conditions. Let's obscured by via question. Then we have 100 uh plus thin B plus C equals the coast sea. This is too small. And this is the capital forecast. It's 28. When we equal 30 let's substitute by vehicle 30. Then we have 108 plus 30 B plus C equals 22. Because there's 22 when we equals 50 let's substitute by 50. Then we have 2508 plus 50 B plus C equals 24. Because there is 24. Let's solve these layers system of equations by eliminating one of the variables. You can easily eliminate C remarkably equation one Bye bye in the swan and added to the equation. Then we have 800 A plus 20 V equals minus 28. 22 is minus six. We can collect equation for it's not to blow equation room by my nice warm. And the added equation three then well 2408 plus for T. V equals minus four. Can call it equation five to solve four and five we can multiply equation two by minus two. Question for. Sorry? Yeah not the black question four by minus two and added to the equation five. Then we have minus 1000 and 600 because 2000 and 400 gives 800. Yeah B is eliminated equals 12 minus four gives a then equals all 0.1. We can substitute an equation for To get beat 800 multiplied by four point oh one. Is it the last 20 B equals minus six. Then B equals minus six minus eight, divided by 20. Then it's minus 4.7 from equation number three you can get see we have 25 plus 50 B 50 multiply by minus 4.7 gives minus 35 plus C equals 24. Then C equals 24 plus 35 minus 25. It's 34. Then C equals 34. And to get the cost function of the velocity, the cost equals all point to one. We square minus 8.7 V plus 34.

Let's take the information from the problem about renting the different RVs and let's translate into equations will at sea equal cost and an equal number of miles. So for stools, for us, if that's how you say it, we have the cost equals point to OM. That would be 20 cents per mile plus 15 45. And for Martin, we have the cost equals 450.30 M. 30 cents per mile, times a number of miles plus 11 83. So here's our system of equations, and I'm going to multiply the second equation by negative one and leave the first equation alone. Or you could do with the other way around. It doesn't matter, and this gives us the opposite of C equals the opposite of 0.30 M. Minus 11 83. And we do this so that we get opposite coefficients on sea. And when we add the equations, the sea terms are eliminated and that gives us zero equals negative. 00.1 om plus 3 62 We can add 0.1 om to both sides and divide by 0.1. And what we find out is that if the mileage is 6000 or so, accuse me 3620. The cost will be the same

Let them know, Mother, my eyes, that is my lead be X. The cost of their truck is $70 that is 7000 tens on their total. But jitters $90 that is 90 Clinton's. So the question is, how many months did destroy that Travels? Who have the cost? Part of my list 40 cents the total of the total but did with this friend should not exceed $90. So let us vote later. That is 7000 cents plus four Titian's into X. This is the total but jack part mile. So next year there's $9000 as it should not x. You there should come under the this change. So after we simply voters, 40 X is equal to 2000 by X is equal, though, tells them by 40 that is 50 so X is equal to 50 miles. So for the, but it'll not exceeds the total budget. The mother for the mileage should be X is less than or the cold of 50 miles. This is the answer