Sunset rents an SUV at$21.95 plus $0.23 per mile. Sunrise rents the same vehicle

Question

Sunset rents an SUV at$21.95 plus $0.23 per mile. Sunrise rents the same vehicle for$24.95 plus $0.19 per mile. For what mileage is the cost thesame? Hint: Using "m" for miles and "c" for cost, write oneequation for each rental company. Then solve the system by one ofthe methods learned in Project 4.02.

Six pears and threeapples cost $3.90. Two pears and five apples cost $3.30. How muchdoes one pear cost? Hint: You have twounknowns (variables), so you need two equations. Write one equationfor each situation and solve the system of equations.

The distance is thesame both upstream and downstream and can be represented by"d." The rate is tricky. The trip downstream (withthe current) is faster than the upstream trip (against thecurrent). We don't know the speed the kayaker makes in still water,so we can represent that with "r."

We do know thatgoing with the current will add 6mph to this rate (r +6), and going against the current will subtract 6mph fromhis rate (r - 6). Now we can write two equations(we have two unknowns). Using d = rt again, theequation upstream is: d = (r - 6)3. You write theequation for the equation downstream, and solve the system. Don'tforget the units in your answer.

5. Your piggy bank has25 coins in it; some are quarters and some are nickels. You have$3.45. How many nickels do you have? (I know you can figure thisout by trial and error, but you must write the equations andsolve.)
   Hint: You have two unknowns:"q" for quarters and "n" fornickels. You need two equations. Write one equation for the numberof coins that you have and a second equation for the value of thecoins. (An unknown number of nickels would have the value of.05n.)

Explanation / Answer

Question #1 $21.95 + $0.23x = $24.95 + $0.19x 0.23x = 3 + 0.19x 0.04x = 3 x = 75 ( to double check, plug 75 back into the orginal equation andmake sure they they cancel out) Question #2 Let x = apples and Y = pears 6x + 3y = 3.9 3x + 5y = 3.3 solve for y in one of the equations. It's not a big deal whichone you solve for because your goin to substitute it into the otherequation 3y = 3.9 - 6x y = (3.9 - 6x)/3 plug y back into the other rquation: 3x +5[(3.9 - 6x)/3] = 3.3 multiply each side by 3 to cancel out the 3 in thedenominator: 3x + 5(3.9-6x) = 9.9 use distributive property and put all variables on 1side: -27x = -9.6 x = -9.6/.27 = 0.36 Question #3 for this problem I would use quess and check 65x =1170   x=18 55x = 990   x =18 Question #4 d = (r-6)3 upstream d = (r+6)2 downstream d = 3r-18 up substitute: 3r-18 = 2r+12 r = 24 Question #5 x = quarter y = nickles .25x + .05y = 3.45 x + y = 25 solve for x in one of the equations x = 25-y plug back into the other equations .25(25-y) + .05y = 3.45 use distributive property 6.25 - .25y + .05y = 3.45 solve for Y: -.20y = -2.8 y = 14 nickels, so X = 11 quarters. Tocheck your answer, plug back into .25x+.05y = 3.45 Question #6 same as question #5 2x + 3.5y = 3825 x+y = 1500 y = 1500-x 2x + 3.5(1500-x) = 3825 2x + 5250 - 3.5x = 3825 -1.5x = -1425 x = 950 students, so y = 550 Question #7 d = (r+25)4 d = (r-25)5 d = 4r + 100 4r+100 = 5r - 125 -r = -225 but spee cant be negative so it is +225 Hope this helped. Don't forget to give Karma please Hope this helped. Don't forget to give Karma please

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