A Course in Game Theory by Rubenstein

By Rubenstein

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If you apply the same operations to the units as you do to the numbers, you’ll find out what units your answer should have. Example Check it out: When you’re writing units, remember that km/hour means the same as (km ÷ hours), and person-days means the same as (persons × days). 2 — Equations 3 Laura drives her car 150 km in 2 hours. Use the formula speed = distance ÷ time to calculate her average speed. Solution speed = distance ÷ time speed = 150 ÷ 2 = 75 Now do the same operations to the units of the numbers: km ÷ hours = km/hour.

In this example you’re figuring out the price of a pen in dollars, so your answer is $2. 7. 2 — Equations You know that six pens and the notebook cost a total of $15. So you can write an equation with the cost of each of the items bought on one side, and the total spent on the other. 6p + 3 = 15 Now you have a two-step equation. You can find the cost of one pen by solving it. 6p + 3 = 15 6p = 12 p=2 One pen costs $2. Guided Practice Write an equation to describe each of the situations in Exercises 1–3.

2 — Equations Subtr act 6 fr om both sides Subtract from Di vide both sides b y 4 Divide by Example 2 Find the value of h when 3h – 11 = 25. Solution In the equation 3h – 11 = 25 the variable h has first been multiplied by 3, and 11 has then been subtracted from the product. So to isolate the variable you must first add 11 to both sides, and then divide them both by 3. 3h – 11 = 25 3h – 11 + 11 = 25 + 11 3h = 36 3h ÷ 3 = 36 ÷ 3 h = 12 Add 11 to both sides Di vide both sides b y3 Divide by Guided Practice Find the value of the variables in Exercises 1–6.

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