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

{{ article.displayTitle }}

Catch-Up and Review

Scaling the Solar System

Different Presentations in Modeling

Scale Drawing

Scale Model

Scale

Using the Scale to Find Actual Dimensions

Hint

Solution

Finding the Scale of a 3D Model

Hint

Solution

Calculating Population Density

Answer

Hint

Solution

Practicing Converting a Scale

Hint

Solution

Practicing Finding or Using the Scale

Calculating the Scale to Choose Better Phone Plan

	{{ 'ml-lesson-number-slides' \| message : article.intro.bblockCount }}
	{{ 'ml-lesson-number-exercises' \| message : article.intro.exerciseCount }}
	{{ 'ml-lesson-time-estimation' \| message }}