Master Scaling, Descriptive Modeling, and Unit Rate

Denoting a Scale
Ratio	$1 in : 100 ft$
Equals Sign	$1 in = 100 ft$
Fraction	$\frac{1 in}{1 0 0 ft}$

Denoting a Scale

Ratio

1 in : 100 ft

Equals Sign

1 in = 100 ft

Fraction

\frac{1 in}{1 0 0 ft}

a Start by writing the dimensions of the walls to be painted. Note that two walls have the same dimensions. This means that they also have the same area.

	Dimensions
Wall $1$	$ℓ_{1} h = 4.75 m = 2.8 m$
Wall $2$	$ℓ_{2} h = 4.75 m = 2.8 m$
Wall $3$	$ℓ_{3} h = 3 m = 2.8 m$

The area of a rectangular wall is found by multiplying the length by the height.

A_{1} = ℓ_{1} \cdot h

SubstituteII

$ℓ_{1} = 4.75 m$ , $h = 2.8 m$

A_{1} = (4.75 m) (2.8 m)

Multiply

A_{1} = 13.3 m^{2}

Remember that Walls

1

and

2

are the same size and have the same area. The area of Wall

3

can be calculated similarly.

A_{3} = (3 m) (2.8 m) = 8.4 m^{2}

Now, to find the total area Mark has to paint, find the sum of the areas of all three walls.

A_{total} = 13.3 + 13.3 + 8.4 = 35 m^{2}

b Saying that

5

square meters can be covered with a liter of paint is equivalent to saying that

\frac{1}{5}

of a liter of paint can cover

1

square meter.

\frac{5 m ^{2}}{liter} \Leftrightarrow \frac{1 liter}{5 m ^{2}}

Multiplying

\frac{1}{5} liters / m^{2}

by the total area gives the number of liters that Mark needs to paint the three walls.

35 m^{2} \cdot \frac{1 liter}{5 m ^{2}} = 7 liters

c Mark needs

7

liters of paint, but each can of paint contains

5

liters. This means that Mark will actually have to buy

2

cans to have enough paint to cover all three walls.

d The cost of the

2

cans can be calculated by multiplying the number of liters in both cans by the price per liter. Each can contains

5

liters, so in total there are

10

liters of paint.

Price of 2 cans = 10 liters \cdot \frac{2 5 dollars}{liter} = 250 dollars

If the paint was sold in

1 -

liter cans, Mark would need to buy

7

cans. In this case, he would pay

7 \cdot 25 = $ 175 .

The amount of money that Mark could have saved can be found by calculating the difference between the price of

10

liters of paint and

7

liters of paint.

250 - 175 = $ 75

Person	Scale of the Plan
Ali	$\frac{$ 1 0}{4 0 min} = $ 0.25$ per minute
Ramsha	$\frac{$ 8}{3 0 min} \approx $ 0.27$ per minute

Person

Scale of the Plan

Ali

\frac{$ 1 0}{4 0 min} = $ 0.25

per minute

Ramsha

\frac{$ 8}{3 0 min} \approx $ 0.27

per minute

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Catch-Up and Review

Explore

Scaling the Solar System

Discussion

Different Presentations in Modeling

Concept

Scale Drawing

Concept

Scale Model

Discussion

Scale

Example

Using the Scale to Find Actual Dimensions

Hint

Solution

Example

Finding the Scale of a 3D Model

Hint

Solution

Example

Calculating Population Density

Answer

Hint

Solution

Example

Practicing Converting a Scale

Hint

Solution

Pop Quiz

Practicing Finding or Using the Scale

Closure

Calculating the Scale to Choose Better Phone Plan

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