1. y = 6x -2 2. y + 2x = 2 If (x,y) is the solution set to the system of equations, then what is the value of x/y?
Let's solve the system of equations by substitution. We'll plug y = 6x -2 into equation 2's y value so equation 2 looks like this after substitution (6x - 2) + 2x = 2 Now solve for x 6x - 2 + 2x = 2 8x - 2 = 2 8x = 4 x = 1/2 Now plug x = 1/2 into y = 6x -2 y = 6 (1/2) - 2 y = 3 - 2 y = 1 Thus x = 1/2 and y = 1 This solves the system of equations but does not solve what the question is asking for. Now let's find the value of x/y x = 1/2 and y = 1 So x/y = 1/2 / 1 x/y = 1/2 Thus the value of x/y is 1/2
Johnson Middle School if planning a field trip to the local zoo. They are trying to figure out how many school buses they will need for the trip. Each school bus costs $150 to operate to the zoo. Johnson Middle School has a total of 2,000 students and teachers. Each bus can hold 62 people. How many buses will be needed for the field trip?
To solve this problem, we divide 62 into 2,000. We reach an answer of 32 remainders 16 Since the remaining 16 people still need a bus to travel to the zoo on, we will need one additional bus Thus the answer is 33 buses. The cost to operate one bus to the zoo is simply extra information not needed to solve this specific problem.
The 4 integers a, a, b, c have an average of 0. Which of the following equations must be true? A. b = c B. b = -a C. b + c = -2a D. b + c = 0 E. b + c = a
The answer is C) b + c = -2a The average is the sum of the terms divided by the number of terms. In this problem the average is 0 so: (a + a + b + c ) / 4 = 0 By combining like terms we reach: 2a + b + c = 0 By re-arranging terms (subtracting 2a from both sides of the equation), we reach answer C): b + c = -2a