Math / Algebra

QuestionMegan creates a scale drawing of a car. The ratio of her scale drawing length to actual car length is $3 \mathrm{~cm}: 2 \mathrm{~m}$ . The length of the car in her drawing is 6 cm .
Ivan draws a scale drawing of the same car. His ratio of scale drawing length to actual car length is $2 \mathrm{~cm}: 1 \mathrm{~m}$ .
What is the length of the car in Ivan's scale drawing?
12 cm 4 cm 3 cm 8 cm

Studdy Solution

STEP 1

What is this asking? If Megan's drawing is 6 cm long and represents a car with a certain scale, how long is Ivan's drawing of the same car with a different scale? Watch out! The scales are different, so don't mix them up!
Also, notice the units are different: cm and m.

STEP 2

1. Find the actual car length
2. Find Ivan's drawing length

STEP 3

Megan's scale is 3 cm : 2 m, and her drawing is 6 cm.
Let's call the actual length of the car $L$ .
We can write this as a proportion: $\frac{3 \text{ cm}}{2 \text{ m}} = \frac{6 \text{ cm}}{L}$

STEP 4

To make things easier, let's convert the meters to centimeters.
Since 1 m = 100 cm, we have 2 m = 200 cm.
Our proportion becomes: $\frac{3 \text{ cm}}{200 \text{ cm}} = \frac{6 \text{ cm}}{L}$

STEP 5

We can cross-multiply: $3 \cdot L = 6 \cdot 200$ $3 \cdot L = 1200$ Now, divide both sides by 3: $L = \frac{1200}{3}$ $L = 400 \text{ cm}$ So, the actual car length is 400 cm, or 4 m.

STEP 6

Ivan's scale is 2 cm : 1 m.
We know the actual car length is 4 m.
Let's call the length of Ivan's drawing $I$ .
The proportion is: $\frac{2 \text{ cm}}{1 \text{ m}} = \frac{I}{4 \text{ m}}$

STEP 7

Cross-multiply: $2 \cdot 4 = 1 \cdot I$ $8 = I$ $I = 8 \text{ cm}$ So, the length of the car in Ivan's scale drawing is 8 cm.

STEP 8

The length of the car in Ivan's scale drawing is 8 cm.

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Studdy Solution

STEP 1

What is this asking? If Megan's drawing is 6 cm long and represents a car with a certain scale, how long is Ivan's drawing of the same car with a different scale? Watch out! The scales are different, so don't mix them up!
Also, notice the units are different: cm and m.

STEP 2

1. Find the actual car length
2. Find Ivan's drawing length

STEP 3

Megan's scale is 3 cm : 2 m, and her drawing is 6 cm.
Let's call the actual length of the car $L$ .
We can write this as a proportion: $\frac{3 \text{ cm}}{2 \text{ m}} = \frac{6 \text{ cm}}{L}$

STEP 4

To make things easier, let's convert the meters to centimeters.
Since 1 m = 100 cm, we have 2 m = 200 cm.
Our proportion becomes: $\frac{3 \text{ cm}}{200 \text{ cm}} = \frac{6 \text{ cm}}{L}$

STEP 5

We can cross-multiply: $3 \cdot L = 6 \cdot 200$ $3 \cdot L = 1200$ Now, divide both sides by 3: $L = \frac{1200}{3}$ $L = 400 \text{ cm}$ So, the actual car length is 400 cm, or 4 m.

STEP 6

Ivan's scale is 2 cm : 1 m.
We know the actual car length is 4 m.
Let's call the length of Ivan's drawing $I$ .
The proportion is: $\frac{2 \text{ cm}}{1 \text{ m}} = \frac{I}{4 \text{ m}}$

STEP 7

Cross-multiply: $2 \cdot 4 = 1 \cdot I$ $8 = I$ $I = 8 \text{ cm}$ So, the length of the car in Ivan's scale drawing is 8 cm.

STEP 8

The length of the car in Ivan's scale drawing is 8 cm.

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Studdy Solution

STEP 1

What is this asking? If Megan's drawing is 6 cm long and represents a car with a certain scale, how long is Ivan's drawing of the *same* car with a *different* scale? Watch out! The scales are different, so don't mix them up!Also, notice the units are different: cm and m.

STEP 2

1. Find the actual car length2. Find Ivan's drawing length

STEP 3

Megan's scale is 3 cm : 2 m, and her drawing is 6 cm.Let's call the actual length of the car LLL.We can write this as a proportion: 3 cm2 m=6 cmL\frac{3 \text{ cm}}{2 \text{ m}} = \frac{6 \text{ cm}}{L}2 m3 cm​=L6 cm​

STEP 4

To make things easier, let's convert the meters to centimeters.Since 1 m = 100 cm, we have 2 m = 200 cm.Our proportion becomes: 3 cm200 cm=6 cmL\frac{3 \text{ cm}}{200 \text{ cm}} = \frac{6 \text{ cm}}{L}200 cm3 cm​=L6 cm​

STEP 5

We can cross-multiply: 3⋅L=6⋅2003 \cdot L = 6 \cdot 2003⋅L=6⋅200 3⋅L=12003 \cdot L = 12003⋅L=1200Now, divide both sides by 3: L=12003L = \frac{1200}{3}L=31200​ L=400 cmL = 400 \text{ cm}L=400 cmSo, the actual car length is **400 cm**, or **4 m**.

STEP 6

Ivan's scale is 2 cm : 1 m.We know the actual car length is 4 m.Let's call the length of Ivan's drawing III.The proportion is: 2 cm1 m=I4 m\frac{2 \text{ cm}}{1 \text{ m}} = \frac{I}{4 \text{ m}}1 m2 cm​=4 mI​

STEP 7

Cross-multiply: 2⋅4=1⋅I2 \cdot 4 = 1 \cdot I2⋅4=1⋅I 8=I8 = I8=II=8 cmI = 8 \text{ cm}I=8 cmSo, the length of the car in Ivan's scale drawing is **8 cm**.

STEP 8

The length of the car in Ivan's scale drawing is **8 cm**.

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What is this asking? If Megan's drawing is 6 cm long and represents a car with a certain scale, how long is Ivan's drawing of the same car with a different scale? Watch out! The scales are different, so don't mix them up!
Also, notice the units are different: cm and m.

1. Find the actual car length
2. Find Ivan's drawing length

Megan's scale is 3 cm : 2 m, and her drawing is 6 cm.
Let's call the actual length of the car $L$ .
We can write this as a proportion: $\frac{3 \text{ cm}}{2 \text{ m}} = \frac{6 \text{ cm}}{L}$

To make things easier, let's convert the meters to centimeters.
Since 1 m = 100 cm, we have 2 m = 200 cm.
Our proportion becomes: $\frac{3 \text{ cm}}{200 \text{ cm}} = \frac{6 \text{ cm}}{L}$

We can cross-multiply: $3 \cdot L = 6 \cdot 200$ $3 \cdot L = 1200$ Now, divide both sides by 3: $L = \frac{1200}{3}$ $L = 400 \text{ cm}$ So, the actual car length is 400 cm, or 4 m.

Ivan's scale is 2 cm : 1 m.
We know the actual car length is 4 m.
Let's call the length of Ivan's drawing $I$ .
The proportion is: $\frac{2 \text{ cm}}{1 \text{ m}} = \frac{I}{4 \text{ m}}$

Cross-multiply: $2 \cdot 4 = 1 \cdot I$ $8 = I$ $I = 8 \text{ cm}$ So, the length of the car in Ivan's scale drawing is 8 cm.

The length of the car in Ivan's scale drawing is 8 cm.