Topic: Help solving word problems!?**Question:**
1. 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 the same?
2. Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.
3. Two cars leave town going opposite directions. One car is traveling 55 mph, and the other is traveling 65 mph How long will it take before they are 180 miles apart?
4. A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.
5. Your piggy bank has 25 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 this out by trial and error, but you must write the equations and solve.)
6. There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?
7. An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air.

June 27, 2019 / By Antonette

I'm not doing all of your homework for you, let alone for free. But I'll help you with some. 1) If you drive m miles, then the cost from Sunset would be 21.95 + 0.23m. If you drive m miles on a car rented from Sunrise, it costs 24.95 + 0.19m. Set those two expressions equal to each other and solve for m. 2) Let "P" be the cost of a pear and "A" the cost of an apple. Then the cost of six pears and three apples is 6P + 3A = 3.90, and two pears plus five apples is 2P + 5A = 3.30. Solve this system for P and A. They want the value of P. 3) Speed is distance over time, so speed times time equals distance. After a time of t hours, the first car is 55t miles away from the starting point, the other is 65t miles away from the starting point. So the distance between them is 55t + 65t. Set this equal to 180 and solve for t.

👍 248 | 👎 10

Did you like the answer? 1) Call number of techs t and helpers h. There are 2 unknowns and 2 relationships: a) t + h = 17 or t = 17 - h b) 210t + 185h = 3345 substitute eq(a) into eq(b): 210(17 - h) + 185h = 3345 3570 - 210h + 185h = 3345 -25h = -225 h = -225/-25 = 9 helpers using eq(a): t = 17 - 9 = 8 techs check using eq(b): 210(8) + 185(9) = 3345 1680 + 1665 = 3345 3345 = 3345 2) 50t + 55t = 367.5 105t = 367.5 t = 367.5/105 = 3.5 hours check: 50(3.5) + 55(3.5) = 367.5 175 + 192.5 = 367.5 367.5 = 367.5 3) x/2 + x/4 + x/12 = x - 30 Put all terms in common denominator then eliminate the denominator: 6x/12 + 3x/12 + x/12 = 12x/12 - 360/12 6x + 3x + x = 12x - 360 10x = 12x - 360 -2x = -360 x = -360/-2 = $180 check: 180/2 + 180/4 + 180/12 = 180 - 30 90 + 45 + 15 = 150 150 = 150 4) Since the size of all batches are equal we call call them all x: 17x + 16x + 18x = 408 51x = 408 x = 408/51 = 8 one-ton batches were bought, or 8 tons check: 17(8) + 16(8) + 18(8) = 408 136 + 128 + 144 = 408 408 = 408 - .--

1.) x+y=17 and 210x + 185y =3345 2) 10(17-y) +185 y=3345 -25y=-225, so y=9 helpers, and 8 technicians. 2.367.5/105=3.5 hours 3) 1/2+1/4+1/12 = 6/12+3/12+1/12=10/12, so if 2/12 =$30.,then 12/12=$180. 4) Since the batches are equal, the average price is $17 a ton. 408/17= 24 tons.

6. There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets? x+y=1500 2x+3.5y=3825 multiply the first eq. by two 2x+2y=3000, now subtract it from the second eq. 2x+3.5y=3825 2x+2y=3000 1.5y=825 y=550 x+550=1500 x=950 5. Your piggy bank has 25 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 this out by trial and error, but you must write the equations and solve.) x+y=25 .05x+.25y=3.45 Apply the same method as above. 4. A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water. 2hrs favor of current *(x+6)=2(x+6) 3 hrs against the current*(x-6)=3(x-3) 2(x+6)=3(x-3) 2x+12=3x-9 21=x rate in still water 7. An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. this one is done the same way as problem #4.

👍 100 | 👎 3

1. let mileage = x. for the cost to be equal, 21.95+0.23x=24.95+0.19x...then x=75 miles. 2. cost of pears = x, cost of apples = y. equation1: 6x+3y=3.9, equation2: 2x+5y=3.3. Therefore one pear costs x= $0.4 or 40 cents. 3. velocity=distance/time...therefore, d=vt. d1=v1*t and d2=v2*t...adding both equations: d1+d2=180= (v1+v2)*t...therefore, t=1.5 hours. 4. The distance the kayaker paddled= x with speed y, x=velocity*t. On the way, x=(y+6)*2...in the return: x=(y-6)*3...The distance x=72 miles and y=30 mph 5. no. of quarters=x, no. of nickels=y. eq1: x+y=25, eq2: 25x+5y=345. x=11 and y=14 6. no of students=x, adults=y. x+y=1500 and 2x+3.5y=3825. x=950 students. 7. just like no. 4, on the way: x=(y+25)*4 and on the return: x=(y-25)*5...the distance x=1000 miles and y=225 mph

👍 91 | 👎 -4

Well, you subtract all the x's you can from one side, leaving one side with a variable and another without. You divide the side with the variable by the side without it. An example would be easier, and this will help you with all other problems: 5x-4-x=3x-6-x -3x -3x 2x-4-x=-6-x +x +x 2x-4=-6 +4 +4 2x=-2 x=-1

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