Math / Algebra

Question6 A science museum has a scale model of a ladybug. In the model, 50 centimeters represents 9 millimeters. The length of the model is 1 meter. How long is the actual ladybug?

Studdy Solution

STEP 1

What is this asking? How many millimeters long is a real ladybug if its 1-meter-long model represents 50 cm for every 9 mm? Watch out! The model and real ladybug lengths are in different units, so we need to be careful!
Also, the model length is given in meters, but the scale is in centimeters.
Don't mix them up!

STEP 2

1. Convert units
2. Set up a proportion
3. Solve for the actual length

STEP 3

Alright, first things first!
We've got a model ladybug that's 1 meter long.
But our scale is in centimeters.
So, let's convert that model length to centimeters.
Remember, there are 100 centimeters in 1 meter.

STEP 4

So, we multiply: $1 \text{ meter} \cdot \frac{100 \text{ centimeters}}{1 \text{ meter}} = 100 \text{ centimeters}.$ Our model is 100 cm long!

STEP 5

Now, the problem tells us that 50 cm on the model represents 9 mm on the actual ladybug.
This gives us a ratio: $\frac{50 \text{ cm (model)}}{9 \text{ mm (actual)}}.$

STEP 6

We want to find out how many millimeters the actual ladybug is if the model is 100 cm.
Let's call the actual length ' $x$ '.
Our proportion is: $\frac{50 \text{ cm}}{9 \text{ mm}} = \frac{100 \text{ cm}}{x \text{ mm}}.$

STEP 7

To solve for $x$ , we can cross-multiply: $50 \cdot x = 9 \cdot 100.$

STEP 8

This simplifies to: $50x = 900.$

STEP 9

Now, we want to isolate $x$ , so we divide both sides by 50: $\frac{50x}{50} = \frac{900}{50}.$

STEP 10

This gives us: $x = \frac{900}{50} = \frac{90}{5} = 18.$

STEP 11

The actual ladybug is 18 mm long!

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Question6 A science museum has a scale model of a ladybug. In the model, 50 centimeters represents 9 millimeters. The length of the model is 1 meter. How long is the actual ladybug?

Studdy Solution

STEP 1

STEP 2

1. Convert units
2. Set up a proportion
3. Solve for the actual length

STEP 3

Alright, first things first!
We've got a model ladybug that's 1 meter long.
But our scale is in centimeters.
So, let's convert that model length to centimeters.
Remember, there are 100 centimeters in 1 meter.

STEP 4

So, we multiply: $1 \text{ meter} \cdot \frac{100 \text{ centimeters}}{1 \text{ meter}} = 100 \text{ centimeters}.$ Our model is 100 cm long!

STEP 5

Now, the problem tells us that 50 cm on the model represents 9 mm on the actual ladybug.
This gives us a ratio: $\frac{50 \text{ cm (model)}}{9 \text{ mm (actual)}}.$

STEP 6

We want to find out how many millimeters the actual ladybug is if the model is 100 cm.
Let's call the actual length ' $x$ '.
Our proportion is: $\frac{50 \text{ cm}}{9 \text{ mm}} = \frac{100 \text{ cm}}{x \text{ mm}}.$

STEP 7

To solve for $x$ , we can cross-multiply: $50 \cdot x = 9 \cdot 100.$

STEP 8

This simplifies to: $50x = 900.$

STEP 9

Now, we want to isolate $x$ , so we divide both sides by 50: $\frac{50x}{50} = \frac{900}{50}.$

STEP 10

This gives us: $x = \frac{900}{50} = \frac{90}{5} = 18.$

STEP 11

The actual ladybug is 18 mm long!

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Question6 A science museum has a scale model of a ladybug. In the model, 50 centimeters represents 9 millimeters. The length of the model is 1 meter. How long is the actual ladybug?

Studdy Solution

STEP 1

STEP 2

1. Convert units2. Set up a proportion3. Solve for the actual length

STEP 3

Alright, first things first!We've got a **model ladybug** that's **1 meter** long.But our scale is in **centimeters**.So, let's convert that model length to centimeters.Remember, there are **100 centimeters** in **1 meter**.

STEP 4

So, we multiply: 1 meter⋅100 centimeters1 meter=100 centimeters.1 \text{ meter} \cdot \frac{100 \text{ centimeters}}{1 \text{ meter}} = 100 \text{ centimeters}.1 meter⋅1 meter100 centimeters​=100 centimeters. Our **model** is **100 cm** long!

STEP 5

Now, the problem tells us that **50 cm** on the **model** represents **9 mm** on the **actual ladybug**.This gives us a ratio: 50 cm (model)9 mm (actual).\frac{50 \text{ cm (model)}}{9 \text{ mm (actual)}}.9 mm (actual)50 cm (model)​.

STEP 6

We want to find out how many millimeters the **actual ladybug** is if the **model** is **100 cm**.Let's call the **actual length** 'xxx'.Our proportion is: 50 cm9 mm=100 cmx mm.\frac{50 \text{ cm}}{9 \text{ mm}} = \frac{100 \text{ cm}}{x \text{ mm}}.9 mm50 cm​=x mm100 cm​.

STEP 7

To solve for xxx, we can **cross-multiply**: 50⋅x=9⋅100.50 \cdot x = 9 \cdot 100.50⋅x=9⋅100.

STEP 8

This simplifies to: 50x=900.50x = 900.50x=900.

STEP 9

Now, we want to **isolate** xxx, so we **divide both sides** by **50**: 50x50=90050.\frac{50x}{50} = \frac{900}{50}.5050x​=50900​.

STEP 10

This gives us: x=90050=905=18.x = \frac{900}{50} = \frac{90}{5} = 18.x=50900​=590​=18.

STEP 11

The actual ladybug is **18 mm** long!

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1. Convert units
2. Set up a proportion
3. Solve for the actual length

Alright, first things first!
We've got a model ladybug that's 1 meter long.
But our scale is in centimeters.
So, let's convert that model length to centimeters.
Remember, there are 100 centimeters in 1 meter.

So, we multiply: $1 \text{ meter} \cdot \frac{100 \text{ centimeters}}{1 \text{ meter}} = 100 \text{ centimeters}.$ Our model is 100 cm long!

Now, the problem tells us that 50 cm on the model represents 9 mm on the actual ladybug.
This gives us a ratio: $\frac{50 \text{ cm (model)}}{9 \text{ mm (actual)}}.$

We want to find out how many millimeters the actual ladybug is if the model is 100 cm.
Let's call the actual length ' $x$ '.
Our proportion is: $\frac{50 \text{ cm}}{9 \text{ mm}} = \frac{100 \text{ cm}}{x \text{ mm}}.$

To solve for $x$ , we can cross-multiply: $50 \cdot x = 9 \cdot 100.$

This simplifies to: $50x = 900.$

Now, we want to isolate $x$ , so we divide both sides by 50: $\frac{50x}{50} = \frac{900}{50}.$

This gives us: $x = \frac{900}{50} = \frac{90}{5} = 18.$

The actual ladybug is 18 mm long!