Module 3 Case Assignment

1. Determine whether the lines will be perpendicular when graphed.
3x-2y=6
-2y = 6 - 3x y = 3x - 3 2
2x+3y=6
3y = 6 - 2x y = - 2x + 2 3
The two lines intercept and they are perpendicular when graphed.

2. Alice’s Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section? x + y = 205 ; x = 2y + 73
2y + 73 + y = 205 x = 2(44) + 73
3y + 73 = 205 x = 88 + 73 = 161
3y = 132 y = 44
44 seats in the smoking section; 161 seats in the non-smoking section
3. Solve the system of equations by the substitution method. x + 3y = 32 ; -3 + 2y = 3 x = 32- 3y x = 32 - 3(9) = 5
-3(32-3y) + 2y = 3
-96 + 9y + 2y = 3
-96 + 11y = 3 y = 9 ; x = 5

4. Solve the system of equations.

x + y = 5 ; x - y = -9

x = 5 - y x = 5 - 7
5 - y - y = -9 x = -2
5 – 2y = -9
-2y = -14 y = 7 ; x = -2

5. Rick’s paint store sells a special shade of pink paint (Ricky’s Blush) which can be made from red paint and white paint. The amount of red paint should be three times the amount of white paint. How much of each kind of paint is needed to make 264 gallons of Ricky’s Blush?

x = white paint
3x = red paint

x + 3x = 264 3(66) = 198
4x = 264 x = 66

66 gallons of white paint; 198 gallons of red paint

A total of 800 tickets were sold for a military ball in support of Fort Lee annual Soldier appreciation week. The non-commissioned officer enlisted Soldier tickets were sold for $20.00 each, and the commissioned officer tickets sold for $25.00 each. The total earnings from ticket sales were $18,500.00. My objective is to determine how many tickets of each type were sold? I set up a system of two equations and two unknowns. I determined utilizing the substitution method that five-hundred (500) non-commissioned officer enlisted Soldier tickets were sold and three-hundred (300) commissioned officer tickets were