submission is used for your score. Answers LarAT9 9.2.050. My Notes Ask Your Tea
ID: 3170044 • Letter: S
Question
submission is used for your score. Answers LarAT9 9.2.050. My Notes Ask Your Teacher Four hundred gallons of 88-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane gasoline (a) Write a system of equations in which one equation represents the amount of final mixture required and the other represents the amounts of 87- and 92-octane gasolines in the final mixture. Let x and y represent the numbers of gallons of 87-octane and 92-octane gasolines, respectively. amount of final mixture required | x + y= 400 amounts of 87- and 92-octane gasolines in the final mixture 87x + 92y = 4001 (b) Use a graphing utility to graph the two equations in part (a) in the same viewing window. As the amount of 87-octane gasoline increases, how does the amount of 92-octane gasoline change? As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline stays the same. As the amount of 87-0ctane gasolline increases, the amount of 92-octane gasoline fluctuates There is not enough information given. As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline increases As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline decreases. (e) How much of each type of gasoline is required to obtain the 400 gallons of 89-octane gasoline? 87-octane 1940 92-octane 1540 x gal x galExplanation / Answer
x + y = 400 is eqn (1)
87x + 92y = 400*88 is eqn (2)
now solve these two equations simultaneously. So, we can get x and y values.
put (1) in (2) such that y = 400-x
==> 87x + 92(400-x) = 400*88
==> 87x + 92*400 - 92x = 400*88
==> 400*(92-88) = 92x - 87x
==> 1600 = 5x
==> x = 320 put this value in (1) to get y.
So, y = 400 -320 ==> y = 80 gallons and x = 320 gallons
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