Wednesday, December 19, 2012

Here's a few examples of some word problems.

Michael has a budget of \$1200 for the golf season. The course he plays costs \$40 for a round of golf. He also wants to takes lessons which costs \$70 each. He wants to play twice as many rounds as lessons taken.

How many rounds of golf can Michael play for the season? How many lessons can he have?

Solution:
Let x = Number of rounds played
x/2 = Number of lessons
Total cost of rounds played plus total number of lessons must be less than or equal to \$1,200.
40x = Total cost of rounds played
70(x/2) = 35x = Total cost of lessons taken
40x + 35x ≤ 1,200
75x ≤ 1,200
x ≤ 16. Therefore, Michael can play 16 times and take 8 lessons for the season

The temperatures on a day in January satisfy the inequality |t - 30| ≤ 12. The temperatures on a day in August satisfy the equation |t - 70| ≤ 16. What are the temperature ranges for January and August and which month has the widest range of temperatures?

Solution:
Solve each inequality.
|t - 30| ≤ 12
Recall for absolute value there is a positive case and a negative case.
The positive case is t - 30 ≤ 12 and the negative case is -12 ≤ t – 30.
t - 30 ≤ 12, -12 ≤ t - 30
t ≤ 42 18 ≤ t
Therefore, the temperature ranges from 18 to 42 in January.
|t - 70| ≤ 16
t - 70 ≤ 16, -16 ≤ t - 70
t ≤ 86 54 ≤ t
Therefore, the temperature ranges from 54 to 86 in August.
The range for January temperatures is 24. (42 - 18 = 24)
The range for August temperatures is 32. (86 - 54 = 32)