LESSON 4 hw

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UNIT 3 : QUADRATIC FUNCTIONS & EQUATIONS

LESSON 4: PROBLEM SOLVING WITH QUADRATIC EQUATIONS HOMEWORK QUESTIONS

Homework Questions:

1. Two numbers have a sum of 40. Find the numbers if their product is 384.

2. A rectangular building measures 14 m by 10 m. It is surrounded by a lawn of uniform width on two sides as shown. The area of this surrounding

lawn equals the area of the building. Find the width of the lawn.

3. Jim and Marie have a lovely swimming pool which measures 12 ft by 6 ft. It is surrounded by a concrete walkway of uniform width.

The area of the walkway equals the area of the swimming pool. Find the width of the walkway.

1. Two numbers have a sum of 40. Find the numbers if their product is 384.

Solution:

à Determine what is unknown or what you are asked to find? Assign variables to the unknowns.

Here we are asked to find two numbers.

Let the first number be x and the second number be y.

à We are told their product is 384. Write this statement as an equation.

à Write this as an equation in one variable.

Since their sum is 40, we have a secondary relation between the two variables.

2. A rectangular building measures 14 m by 10 m. It is surrounded by a lawn of uniform width on two sides as shown. The area of this surrounding

lawn equals the area of the building. Find the width of the lawn.

Solution:

à Determine what is unknown or what you are asked to find? Assign variables to the unknowns.

Here we are asked to find the width of the lawn.

Let the width of the lawn be x metres. See diagram.

Therefore the length of the larger rectangle will be (14 + x) and its width will be (10 + x)

The area of the smaller rectangle is 14 x 10 = 140 m². The area of the uniform lawn is the same 140 m².

Therefore the area of the larger rectangle will be 140 + 140 = 280 m². The following equation results.

Solution:

à Determine what is unknown or what you are asked to find? Assign variables to the unknowns.

Here we are asked to find the width of the walkway.

Let the width of the walkway be x feet. See diagram.

Therefore the length of the larger rectangle will be (32 +2x) and its width will be (16 + 2x)

The area of the smaller rectangle is 32 x 16 = 512 ft². The area of the uniform walkway is the same 512 ft².

Therefore the area of the larger rectangle will be 512 + 512 = 1024 ft². The following equation results.