Problem Solving Assignment
Quadratic Equations
{Full Solutions for Full Marks}
1. A cylindrical popcorn container has a height of 30 cm and a surface area of 4 241 square centimeters. Find
the radius of the cylinder, to the nearest tenth of a centimeter. [5]
2. A bakery sells 50 loaves a day of a particular bread at $1.50 a loaf. Research indicates that, for every 10¢
increase in the price, two fewer loaves would be sold. An equation for the daily revenue is R  0.2 x 2  2 x  75
where x represents the number of 10¢ increases.
a) Use this equation to find the number of 10¢ increases that will result in daily revenue of $80. [3]
b) What is the new price of a loaf of bread? [1]
c) What price(s) for a loaf of bread would give a daily income of at least $79.20? [4]
3. You have an empty 7L pail, an empty 3L pail, and a 10L pail full of water. There are no volume markings on
the pails. In one pouring, you can fill or empty a pail by pouring water from one pail to another. What is the
smallest number of pourings needed to get 5L of water in the 10L pail and 5L of water in the 7L pail? [5]
4. Find two rectangles (with non-zero, integral sides) whose area and perimeter are the same. [4]
5. In nature, as in human-made design, geometry’s role is aesthetic, strengthening, structural, and functional. The
positive Golden Ratio value is a ratio of dimensions that is found in seed growth, body proportions, and architecture.
The Greek letter phi (𝜑) is used to represent the ratio. A golden rectangle is a rectangle where the length to width
ratio is 1 to 𝜑.
a) Solve the equation 𝜑 2– 𝜑 –1=0 to find both the exact value and the approx value (to 6 decimals) of the
golden ratio. [3]
b) If a golden rectangle is 36cm wide, calculate the length to 2 decimal places. [1]
c) The Fibonacci sequence of numbers begins 1,1,2,3,5,8,13,21,... . Each subsequent term is found by adding the
two terms before it. The ratio of the two consecutive Fibonacci numbers 13 and 21 gives 1.615 384…, which
correctly shows the first three digits of the Golden Ratio. Which two consecutive Fibonacci numbers
correctly show the first six digits of 𝜑? [3]
6. A trucker drives a distance of 480km. She leaves at the same time as another driver in a jeep. The jeep travels an
average speed of 20km/h faster than the truck. The jeep arrives at their common destination 2h sooner than the truck.
How fast, on average, did each go? Provide an algebraic solution. [5]
7. Determine the exact value(s) of k if
a) 2 x 2  kx  9  0 has equal roots.
b) 4x2 + kx + 7 = 0 has two imaginary roots.
[2]
[2]
Group Members: ________________________________________________
Problem Solving Assignment
Quadratic Equations
{Full Solutions for Full Marks}
1. A cylindrical popcorn container has a height of 30 cm and a surface area of 4 241 square centimeters. Find
the radius of the cylinder, to the nearest tenth of a centimeter. [5]
2. A bakery sells 50 loaves a day of a particular bread at $1.50 a loaf. Research indicates that, for every 10¢
increase in the price, two fewer loaves would be sold. An equation for the daily revenue is R  0.2 x 2  2 x  75
where x represents the number of 10¢ increases.
a) Use this equation to find the number of 10¢ increases that will result in daily revenue of $80. [3]
b) What is the new price of a loaf of bread? [1]
c) What price(s) for a loaf of bread would give a daily income of at least $79.20? [4]
3. You have an empty 7L pail, an empty 3L pail, and a 10L pail full of water. There are no volume markings on
the pails. In one pouring, you can fill or empty a pail by pouring water from one pail to another. What is the
smallest number of pourings needed to get 5L of water in the 10L pail and 5L of water in the 7L pail? [5]
4. Find two rectangles (with non-zero, integral sides) whose area and perimeter are the same. [4]
5. In nature, as in human-made design, geometry’s role is aesthetic, strengthening, structural, and functional. The
positive Golden Ratio value is a ratio of dimensions that is found in seed growth, body proportions, and architecture.
The Greek letter phi (𝜑) is used to represent the ratio. A golden rectangle is a rectangle where the length to width
ratio is 1 to 𝜑.
a) Solve the equation 𝜑 2– 𝜑 –1=0 to find both the exact value and the approx value (to 6 decimals) of the
golden ratio. [3]
b) If a golden rectangle is 36cm wide, calculate the length to 2 decimal places. [1]
c) The Fibonacci sequence of numbers begins 1,1,2,3,5,8,13,21,... . Each subsequent term is found by adding the
two terms before it. The ratio of the two consecutive Fibonacci numbers 13 and 21 gives 1.615 384…, which
correctly shows the first three digits of the Golden Ratio. Which two consecutive Fibonacci numbers
correctly show the first six digits of 𝜑? [3]
6. A trucker drives a distance of 480km. She leaves at the same time as another driver in a jeep. The jeep travels an
average speed of 20km/h faster than the truck. The jeep arrives at their common destination 2h sooner than the truck.
How fast, on average, did each go? Provide an algebraic solution. [5]
7. Determine the exact value(s) of k if
a) 2 x 2  kx  9  0 has equal roots.
b) 4x2 + kx + 7 = 0 has two imaginary roots.
[2]
[2]
Group Members: ________________________________________________