7.4 Applying Linear Equations

7.4 – Applying Equations Goals / “I can…”  Write systems of linear equations

7.4 – Applying Equations We have 3 ways to solve a linear system.  Graph  Substitution  Elimination You may select ANY of these ways when solving a real world problem.

7.4 – Applying Equations We will now work on story problems that relate to a linear system. The book suggests that you break the problem into 3 parts to set up the system. 1.Define 1.Define – write down the variables. (Hint, the variables are what the question is asking for.) 2.Relate 2.Relate – How do the variables relate in the problem. (Hint – relate apples to apples.) 3.Write 3.Write – Write down the equations into a system

7.4 – Applying Equations Example 1 A chemist has one solution that is 50% acid. She has another solution that is 25% acid. How many liters of each type of acid solution should she combine to get 10 liters of a 40% acid.

7.4 – Applying Equations Define – x = 50% acidy = 25% acid Relate – How many liters How many liters of acid. Write - x + y = 10.50x +.25y = 10(.40) x + y = 10.50x +.25y = 10(.40) How would you solve this?

7.4 – Applying Equations Suppose you combine ingots of 25% copper alloy and 50% copper alloy to create 40kg of 45% copper alloy. How many kilograms of each do you need?

7.4 – Applying Equations Example 2: Suppose you have a typing service. You buy a personal computer for $1750 on which to do your typing. You charge $5.50 per page of typing. Expenses are $.50 per page for ink, paper, electricity and other expenses. How many pages must you type to break even?

7.4 – Applying Equations Define - x = # of copies y = amount of money Relate - Expense amountincome amount Write - y = $ $.50xy = $5.50x y = $ $.50x y = $5.50x How would you solve this?

7.4 – Applying Equations Example 3: Suppose it takes you 6.8 hours to fly about 2800 miles from Miami to Seattle. At the same time, your friend files from Seattle to Miami. His planes travels with the same average airspeed, but his fight only take 5.6 hours. Find the average airspeed of the planes and the average wind speed.

7.4 – Applying Equations Define - x = airspeedy = wind speed Relate - flight to Seattle flight to Miami Write - (x – y)6.8 = 2800 (x + y)5.6 = 2800