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.GraphSubstitutionElimination
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.1.1. DefineDefine – write down the variables. (Hint, the
variables are what the question is asking for.)
2.2. RelateRelate – How do the variables relate in the problem. (Hint – relate apples to apples.)
3.3. WriteWrite – 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% acid y = 25% acidRelate – 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?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: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 amount income amount
Write - y = $1750 + $.50x y = $5.50x
y = $1750 + $.50xy = $5.50x
How would you solve this?How would you solve this?
7.4 – Applying Equations
Example 3: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 = airspeed y = wind speed
Relate - flight to Seattle flight to Miami
Write - (x – y)6.8 = 2800 (x + y)5.6 = 2800
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