sample questions 91587. example 1 billys restaurant ordered 200 flowers for mothers day. they...
TRANSCRIPT
Sample Questions
91587
Example 1
• Billy’s Restaurant ordered 200 flowers for Mother’s Day.
• They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.
• They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $589.50. How many of each type of flower was ordered?
Decide your variables
• Billy’s Restaurant ordered 200 flowers for Mother’s Day.
• They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.
• They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $589.50. How many of each type of flower was ordered?
Write the equations
• Billy’s Restaurant ordered 200 flowers for Mother’s Day. c + r + d = 200
• They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.
• 1.5c + 5.75r + 2.6d = 589.50 • They ordered mostly carnations, and 20 fewer
roses than daisies. d – r = 20• The total order came to $589.50. • How many of each type of flower was ordered?
Order the equations
• Billy’s Restaurant ordered 200 flowers for Mother’s Day. c + r + d = 200
• They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.
• 1.5c + 5.75r + 2.6d = 589.50 • They ordered mostly carnations, and 20 fewer
roses than daisies. d – r = 20• The total order came to $589.50. • How many of each type of flower was ordered?
Solve using your calculator and answer in context
• There were 80 carnations, 50 roses and 70 daisies ordered.
Example 2
• If possible, solve the following system of equations and explain the geometrical significance of your answer.
Calculator will not give you an answer.
• If possible, solve the following system of equations and explain the geometrical significance of your answer.
Objective - To solve systems of linear equations in three variables.
Solve.
There is no solution. The three planes form a tent shape and the lines of intersection of pairs of planes are parallel to one another
Inconsistent, No Solution
Example 2
• Solve the system of equations using Gauss-Jordan Method
Example
• Solve the system of equations using Gauss-Jordan Method
Example
• Solve the system of equations using Gauss-Jordan Method
Example
• Solve the system of equations using Gauss-Jordan Method
Example
• Solve the system of equations using Gauss-Jordan Method
No solution
Example 3
Consider the following system of two linear equations, where c is a constant: 1. Give a value of the constant c for which the
system is inconsistent. 2. If c is chosen so that the system is consistent,
explain in geometrical terms why there is a unique solution.
Give a value of the constant c for which the system is inconsistent.
The lines must be parallel but not a multiple of each other
c = 10
If c is chosen so that the system is consistent, explain in geometrical terms why there is a unique solution.
It means that the 2 lines must have different gradients so they intersect to give a unique solution.
Example 4
• The Health Club serves a special meal consisting of three kinds of food, A, B and C. Each unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of protein. Each unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of protein. Each unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of protein. The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein. Let a, b and c be the number of units of food A, B and C f respectively) used in the special meal. Set up a system of 3 simultaneous equations relating a, b and c.
• Do not solve the equations.
For this type of problem it is easier if you make a table
• The Health Club serves a special meal consisting of three kinds of food, A, B and C. Each unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of protein. Each unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of protein. Each unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of protein. The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein. Let a, b and c be the number of units of food A, B and C f respectively) used in the special meal. Set up a system of 3 simultaneous equations relating a, b and c.
• Do not solve the equations.
Carbohydrate Fat ProteinABC
Each unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of protein
Carbohydrate Fat ProteinA 20 2 4BC
Each unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of protein
Carbohydrate Fat ProteinA 20 2 4B 5 1 2C
Each unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of protein
Carbohydrate Fat ProteinA 20 2 4B 5 1 2C 80 3 8
The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein.
Carbohydrate Fat ProteinA 20 2 4B 5 1 2C 80 3 8Total 140 11 24
Write the equations
Carbohydrate Fat ProteinA 20 2 4B 5 1 2C 80 3 8Total 140 11 24
Example 5
Consider the following system of three equations in x, y and z.
4x + 3y + 2z = 113x + 2y + z = 8 7x + 5y + az = b
Give values for a and b in the third equation which make this system:1. inconsistent, 2. consistent, but with an infinite number of solutions.
Inconsistent
Add the first two equations and put it with the third equation
4x + 3y + 2z = 113x + 2y + z = 8 7x + 5y + 3z = 19
7x + 5y + az = b
• a = 3, b ≠19
Consistent with an infinite number of solutions
Add the first two equations and put it with the third equation
4x + 3y + 2z = 113x + 2y + z = 8 7x + 5y + 3z = 19
7x + 5y + az = b
• a = 3, b = 19
Example 6
Consider the following system of three equations in x, y and z.• 2x + 2y + 2z = 9• x + 3y + 4z = 5 • Ax + 5y + 6z = BGive possible values of A and B in the third equation which make this system:1. inconsistent.2. consistent but with an infinite number of solutions.
Example 6
• 2x + 2y + 2z = 9 • x + 3y + 4z = 5 3x + 5y + 6z = 14• Ax + 5y + 6z = B Ax + 5y + 6z = B
1. inconsistent. A = 3, B ≠ 142. consistent but with an infinite number of solutions. A = 3, B = 14