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)

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