Answer/Discussion on Introduction to Problem Solving

(Back to the tutorial on introduction to problem solving)

Beginning Algebra
Answer/Discussion to Practice Problems
on Introduction to Problem Solving

Answer/Discussion to 1a

The sum of a number and 2 is 6 less than twice that number.

Step 1: Understand the problem.

Make sure that you read the question carefully several times.

Since we are looking for a number, we will let

x = a number

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

*Get all the x terms on one side

*Inv. of add 2 is sub. 2

*Inv. of mult. by -1 is div. by -1

Step 4: Look back (check and interpret).

If you take the sum of 8 and 2 it is 6 less than twice 8, so this does check.

FINAL ANSWER:

The number is 8.

(return to problem 1a)

Answer/Discussion to 1b

A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.

Step 1: Understand the problem.

Make sure that you read the question carefully several times.

We are looking for the length and width of the rectangle. Since width can be written in terms of length, we will let

L = length

Width is 8 feet less than twice the length:

2L - 8 = width

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

*Mult. ( ) by 2
*Combine like terms

*Inv. of sub. 16 is add 16

*Inv. of mult. by 6 is div. by 6

Step 4: Look back (check and interpret).

If length is 6, then width, which is 8 feet less than twice the length, would have to be 4. The perimeter of a rectangle with width of 4 feet and length of 6 feet is 20 feet.

FINAL ANSWER:

Width is 4 feet.

Length is 6 feet.

(return to problem 1b)

Answer/Discussion to 1c

Complimentary angles, sum up to be 90 degrees. Find the measure of each angle in the figure below. Note that since the angles make up a right angle, they are complementary to each other.