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#### • how to solve an elimination problem

Question:heres the problem: Each family in a neighborhood is contributing $20 worth of food to the neighborhood picnic. The Harlin family is bringing 12 packages of buns. The hamburger buns cost$2.00 per package. The hot-dog buns cost $1.50 per package. How many packages of each type of bun did they buy? plz show your work and explain thanks Answers:x + y = 12 2x + 1.5y = 20 Solve by elimination. x+y= 12 (2) 2x + 2y = 24 2x + 1.5y = 20 ---------------------- .5y = 4 y = 8 2x + 1.5(8) = 20 2x + 12 = 20 2x = 8 x = 4 4+ 8 = 12 8 + 12 = 20 Question:Theater Productions: At a recent production of A Comedy of Errors, the Community Theater brought in a total of$30,495 in revenue. If adult tickets were $9 and children ticket were$6.50, how many tickets of each type were sold if 3800 tickets in all were sold? never mind you don't have to answer i just found out how to do it ..u can answer to get free points if you want hehe srry

Answers:Equations: 1) 9a+6.5c=30495 2) a+c=3800 Eliminate c: 1) 9a+6.5c=30495 2) x -6.5: -6.5a-6.5c=-24700 _________________________ 2.5a =5795 a=2318 Sub a=2318 into 2: a+c=3800 2318+c=3800 c=1482 Check: 2318+1482=3800 (Correct) Therefore, 2318 adult tickets and 1482 child tickets were sold. Grade 10 mathematics, right? I just finished this unit. Hope I helped!

Question:Eliminations 23. 2x-2y=-8 x+2y=-1 24. 5x+8y=-29 7x-2y=-67 25. 3x-4y=-24 x+y=-1 26.-10x-3y=-18 -7x-8y=11 Simplify each expression 27. (7.46)^-5 x (7.46)^6 28.a^5 x 3b^9 x 6a 29.-4x^3 x 2y^-2 x 5y^5 x x^-8 30.6 x 6^1-2 x 6^1 31. (x^9)^0(x^7)^2 32.(5k^2)^3 33.(-5g^5h^6)^2(g^4h^2)^4 34.9^7 ____(fraction) 9^9 19.Write an equation for the line that is parallel to the given line and that passes through the given point. y=-5x+3;(-6,3) 46.Use the quadratic formula to solve the equation round to the nearest 10th 2a-46a+252=0 47. Use any method to solve round to the nearest 10th 7x^2-16x=8 Word Problems 55.The top speed of a certain bicyclist is 30 miles per hour.What is the top speed of the bicyclist per second? 56.Leon's cell phone company charges $20 per month plus$0.30 per minute of usage for anytime minutes over 100 minutes.Another cell phone company charges \$59 per month for Unlimited usage.How many minutes would leon have to use under his plan before it would be cheaper for him to use the other company? 56.The width of a regulation feild on which field hockey is played is 60 yards.The length of the feild is 100 yards.The feild is typically divided into 4 zones each with a length of 25 yards.Your park distrivt wants to construct a field hockey pratice field that has dimensions 3/5 to dimensions a regulation feild. part a--explain how to find the dimension of the pratice field your park district wants to construct. please help me , you dont have to do all of them just the ones you know.amd sorry for the typos

Answers:27. (7.46)^-5 x (7.46)^6. With multiplication, add the indices: 7.46 ^ (-5+6) = 7.46^1 = 7.46 28.a^5 x 3b^9 x 6a group common variables: 6a^6 x 3b^9 29.-4x^3 x 2y^-2 x 5y^5 x x^-8 = (-4x^3 x x^-8) x (2y^-2 x 5y^5) = -4x^-5 x 10y^3 30. 6 x 6^1-2 x 6^1 6^1(6 - 2) 6^1*4 = 24 or 6 x 6^1-2 x 6^1 = 6^2 - 2 x 6 = 36 - 12 = 24 (-5g^5h^6)^2(g^4h^2)^4 =25g^10 h ^12 g^16 h^8 = 25 g^26 h^20 31. (x^9)^0(x^7)^2 anything ^0 = 1, so the answer is x^14. 55. You need to convert the speed from miles per hour to feet per second. there are 5280 ft per mile and 3600 s/hr: 30miles per hour = 30miles / h * 5280 ft / mile / 3600 s/hr = 158 400 ft/h / 3600s/hr = 44ft / s 56. Find an equation for the Cost C = 20 + 0.3t the break even point is when C = 59, the offer from the other company. Set C = 59 and solve for t: 59 = 20 + 0.3t 39 = 0.3t t = 130minutes

Question:okay heres the quesiton: You drive a car that runs on ethanol and gas. you have a 20-gallon tank to fill and you can buy fuel that is either 25 percent ethanol or 85 percent ethanol. How much of each type of fuel should you buy to fill your tank so that it is 50 percent ethanol? Really Appreciate It.

Answers:Let's say we need x gallons of 25 percent ethanol and y gallons of 85 percent ethanol. The tank is 20 gallons and it needs to be filled, which means there will be 20 gallons total, so we can write: x + y = 20 Now, we have x gallons of 25 percent ethanol, which is 0.25x gallons of pure ethanol. We also have y gallons of 85 percent ethanol, which is 0.85y more gallons of pure ethanol. So, the total amount of pure ethanol is 0.25x+0.85y. We want the fuel to be 50% ethanol, so we want the amount of pure ethanol divided by the total amount of fuel to be 0.5. Since there are 0.25x+0.85y gallons of pure ethanol and 20 total gallons of fuel, we have: (0.25x + 0.85y)/20 = 0.5 Multiplying by 20, we get: 0.25x + 0.85y = 10 So, we have this system of equations: x + y = 20 0.25x + 0.85y = 10 To use elimination, we need both equations to have the same coefficient for one of the variables. In the first equation, the coefficient of x is 1. We can make the coefficient of x in the second equation be 1 by multiplying by 4: 0.25x + 0.85y = 10 x + 3.4y = 40 Now we can subtract the first equation from that: (x + 3.4y) - (x + y) = 40 - 20 x + 3.4y - x - y = 20 2.4y = 20 y = 25/3 Now we can solve for x by plugging that into the first equation: x + y = 20 x + 25/3 = 20 x = 35/3 So, you should buy 35/3 gallons of 25% ethanol and 25/3 gallons of 85% ethanol. That's 11 2/3 gallons of 25% ethanol and 8 1/3 gallons of 85% ethanol. Hope that helps :)