1 sections 1.4: rewriting equations and formulas section 1.5: problem solving what you will learn:...

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Sections 1.4: Rewriting Equations and FormulasSection 1.5: Problem Solving

What you will learn:1. How to solve for a single variable2. How to develop an algebraic equations (or…the dreaded word problem)

Objective: Section 1.4 - Rewriting Equations and Formulas, 1.5 - Problem Solving

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Rewriting Formulas and EquationsSolve 7x – 3y = 8 for y


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You Try 11x – 9y = -4 solve for y


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Substituting and Solving for a Variable

Sometimes substituting values for variables is easier when you solve for a variable. For example:

Give the equation x + xy = 1, find the value of y when

x = -1 and x = 3.

Step 1: solve for y

Step 2: substitute


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You Try Given the equation xy – x = 4, find the

value of y when x = -4 and x = 2. Step 1, solve for y

Step 2, substitute


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Word ProblemsYou are putting on a concert. Your goal is to sell $25,000 in

tickets. You plan to charge $25.25 per adult and expect to sell 800 adult tickets. You need to determine what to charge for child tickets. How much should you charge if you plan to sell 200 child tickets? 300? 400?

R = Revenue p1 = price for adult p2 = price for child

A = number of adult tickets C = number of child tickets


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You TryYou are selling two types of caps – basic and deluxe. Write

a revenue equation for this scenario.

You expect to sell 125 of the basic hats at $8.00 each. To meet your goal of $1600 in sales, what would you need to charge for the deluxe hats if you can sell 50? 60?


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Rewriting Common Formulas The formula for perimeter is p = 2l + 2w.

Solve for w.


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You Try Solve Einstein’s energy formula E = mc2

for m, mass


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Expressing One Variable in Terms of Another

Sometimes we need to express a variable in terms of another variable. Example: You have 40 feet of fencing with which to enclose a rectangular garden. Express the garden’s area in terms of its length only.

A = lw


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Algebraic Models

Verbal Model – an equation in words or…a word problem.Algebraic Model – The word problem as a mathematical statement.


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Tons of Word Problems The Bullet Train runs between the Japanese cities of

Osaka and Fukuoka, a distance of 550 kilometers. When it makes no stops, it takes 2 hours and 15 minutes to make the trip. What is the average speed of the Bullet Train?

Distance = Rate x Time Labels Distance = 550

Rate = r

Time = 2.25


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You Try On August 15, 1995 the Concorde flew

35,035 mi from New York City to New York City in 31 hours, 27 minutes. What was the average speed?

Distance = Rate x Time Labels:


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Looooong Word ProblemsExample 4 on page 35.

Step 1, Draw a picture:

Step 2, Verbal Model:

Step 3, Labels:

Total miles of track = 1590 Union Pacific rate = 20

Central Pacific rate = 8.75 Union Pacific time = t - 24

Central Pacific time = t

Step 4, Algebraic Model:


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You Try A fire truck is called to a scene. Three minutes later, a

second truck is called. The first truck averages only 30 mph, but the second truck averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel?

Verbal Model: Labels:

Algebraic Model:


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Algebraic Model from a Pattern The table gives the heights to the top of the first few

stories of a tall building. Determine the height to the top of the 15th story.

Verbal Model: Labels:

Algebraic Model:

Story Lobby 1 2 3 4Height to top of story in feet

20 32 44 56 68


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Using Formulas with Word Problems A spherical weather balloon needs to hold 175 cubic feet of

helium to be buoyant enough to lift an instrument package to a desired height. To the nearest tenth of a foot, what is the radius of the balloon.

3

3

4rV


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Homework Page 29, problems 14, 22, 24, 26, 28 and

30 Page 37, problems 8-11 all, 18

Quiz: Open NoteConcentrate on:Identifying types of numbersIdentifying propertiesSolving equations

1 sections 1.4: rewriting equations and formulas section 1.5: problem solving what you will learn:...

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