Math / Geometry

QuestionMr. Perez used a map to find out how far it is between two cities. On the map, the distance between the two citles is 4 inches. The actual distance between the cities is 300 miles.
What was the scale on the map that was used to calculate the distance between the two citles? 1 inch represents 150 miles 75 inches represents 1 mile 1 inch represents 75 miles 1 inch represents 1 mile

Studdy Solution

STEP 1

What is this asking? If 4 inches on a map represents 300 miles in real life, how many miles does 1 inch on the map represent? Watch out! Don't mix up inches and miles!
We need to find the number of miles per inch, not inches per mile.

STEP 2

1. Set up a proportion
2. Solve for the unknown

STEP 3

Alright, let's rock this map problem!
We know that 4 inches on the map equals 300 miles in real life.
We can write this as a fraction: $\frac{4 \text{ inches}}{300 \text{ miles}}$ .
This fraction represents the ratio of map distance to real distance.

STEP 4

We want to find how many miles 1 inch on the map represents.
Let's call this unknown number of miles " $x$ ".
We can write another fraction for this: $\frac{1 \text{ inch}}{x \text{ miles}}$ .

STEP 5

Now, here comes the magic of proportions!
We set these two fractions equal to each other, because the scale of the map stays the same: $\frac{4 \text{ inches}}{300 \text{ miles}} = \frac{1 \text{ inch}}{x \text{ miles}}$

STEP 6

To solve for $x$ , we can cross-multiply.
This gives us: $4 \text{ inches} \cdot x \text{ miles} = 300 \text{ miles} \cdot 1 \text{ inch}$ $4x = 300$

STEP 7

Now, we want to get $x$ all by itself.
Since $x$ is being multiplied by 4, we'll divide both sides of the equation by 4: $\frac{4x}{4} = \frac{300}{4}$ $x = 75$

STEP 8

So, $x = \mathbf{75}$ miles.
This means 1 inch on the map represents 75 miles in real life!

STEP 9

The scale of the map is 1 inch represents 75 miles.

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Studdy Solution

STEP 1

What is this asking? If 4 inches on a map represents 300 miles in real life, how many miles does 1 inch on the map represent? Watch out! Don't mix up inches and miles!
We need to find the number of miles per inch, not inches per mile.

STEP 2

1. Set up a proportion
2. Solve for the unknown

STEP 3

Alright, let's rock this map problem!
We know that 4 inches on the map equals 300 miles in real life.
We can write this as a fraction: $\frac{4 \text{ inches}}{300 \text{ miles}}$ .
This fraction represents the ratio of map distance to real distance.

STEP 4

We want to find how many miles 1 inch on the map represents.
Let's call this unknown number of miles " $x$ ".
We can write another fraction for this: $\frac{1 \text{ inch}}{x \text{ miles}}$ .

STEP 5

Now, here comes the magic of proportions!
We set these two fractions equal to each other, because the scale of the map stays the same: $\frac{4 \text{ inches}}{300 \text{ miles}} = \frac{1 \text{ inch}}{x \text{ miles}}$

STEP 6

To solve for $x$ , we can cross-multiply.
This gives us: $4 \text{ inches} \cdot x \text{ miles} = 300 \text{ miles} \cdot 1 \text{ inch}$ $4x = 300$

STEP 7

Now, we want to get $x$ all by itself.
Since $x$ is being multiplied by 4, we'll divide both sides of the equation by 4: $\frac{4x}{4} = \frac{300}{4}$ $x = 75$

STEP 8

So, $x = \mathbf{75}$ miles.
This means 1 inch on the map represents 75 miles in real life!

STEP 9

The scale of the map is 1 inch represents 75 miles.

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Studdy Solution

STEP 1

What is this asking? If 4 inches on a map represents 300 miles in real life, how many miles does 1 inch on the map represent? Watch out! Don't mix up inches and miles!We need to find the number of miles per inch, not inches per mile.

STEP 2

1. Set up a proportion2. Solve for the unknown

STEP 3

Alright, let's **rock** this map problem!We know that 4 inches on the map equals 300 miles in real life.We can write this as a **fraction**: 4 inches300 miles\frac{4 \text{ inches}}{300 \text{ miles}}300 miles4 inches​.This fraction represents the **ratio** of map distance to real distance.

STEP 4

We want to find how many miles 1 inch on the map represents.Let's call this unknown number of miles "xxx".We can write another **fraction** for this: 1 inchx miles\frac{1 \text{ inch}}{x \text{ miles}}x miles1 inch​.

STEP 5

Now, here comes the **magic** of proportions!We set these two fractions **equal** to each other, because the scale of the map stays the same: 4 inches300 miles=1 inchx miles \frac{4 \text{ inches}}{300 \text{ miles}} = \frac{1 \text{ inch}}{x \text{ miles}} 300 miles4 inches​=x miles1 inch​

STEP 6

To solve for xxx, we can **cross-multiply**.This gives us: 4 inches⋅x miles=300 miles⋅1 inch 4 \text{ inches} \cdot x \text{ miles} = 300 \text{ miles} \cdot 1 \text{ inch} 4 inches⋅x miles=300 miles⋅1 inch 4x=300 4x = 300 4x=300

STEP 7

Now, we want to get xxx all by itself.Since xxx is being multiplied by **4**, we'll **divide both sides** of the equation by **4**: 4x4=3004 \frac{4x}{4} = \frac{300}{4} 44x​=4300​ x=75 x = 75 x=75

STEP 8

So, x=75x = \mathbf{75}x=75 miles.This means 1 inch on the map represents **75** miles in real life!

STEP 9

The scale of the map is 1 inch represents 75 miles.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? If 4 inches on a map represents 300 miles in real life, how many miles does 1 inch on the map represent? Watch out! Don't mix up inches and miles!
We need to find the number of miles per inch, not inches per mile.

1. Set up a proportion
2. Solve for the unknown

Alright, let's rock this map problem!
We know that 4 inches on the map equals 300 miles in real life.
We can write this as a fraction: $\frac{4 \text{ inches}}{300 \text{ miles}}$ .
This fraction represents the ratio of map distance to real distance.

We want to find how many miles 1 inch on the map represents.
Let's call this unknown number of miles " $x$ ".
We can write another fraction for this: $\frac{1 \text{ inch}}{x \text{ miles}}$ .

Now, here comes the magic of proportions!
We set these two fractions equal to each other, because the scale of the map stays the same: $\frac{4 \text{ inches}}{300 \text{ miles}} = \frac{1 \text{ inch}}{x \text{ miles}}$

To solve for $x$ , we can cross-multiply.
This gives us: $4 \text{ inches} \cdot x \text{ miles} = 300 \text{ miles} \cdot 1 \text{ inch}$ $4x = 300$

Now, we want to get $x$ all by itself.
Since $x$ is being multiplied by 4, we'll divide both sides of the equation by 4: $\frac{4x}{4} = \frac{300}{4}$ $x = 75$

So, $x = \mathbf{75}$ miles.
This means 1 inch on the map represents 75 miles in real life!