QuestionUsing the information from the question above, is the scale drawing larger than the actual spider?
is Larger then actual Size Larger
If the distance from Haley's house to school is $2.5$ centimeters on the map and the actual distance is $3$ miles, what is the scale for the map?
A house blueprint shows the bedroom is $4$ inches wide. Its actual length is $12$ yards wide. What is the scale for the blueprint?
Jimmy is $6$ feet tall and casts a $10$ foot shadow. Nikki casts a $9$ foot shadow. How tall is Nikki?
Cammy is standing next to a pine tree. The tree is $25$ foot tall and casts a $20$ foot shadow. Cammy casts a $5$ foot shadow. How tall is Cammy?

Studdy Solution

STEP 1

What is this asking? We've got a bunch of word problems all about scales, ratios, and proportions!
We need to figure out if a drawing is bigger than a real spider, find the scale of a map and a blueprint, and then solve how tall two people are based on their shadows. Watch out! Make sure your units match up when you're setting up your proportions!
Don't compare inches to miles without converting one of them first.

STEP 2

1. Spider size
2. Map scale
3. Blueprint scale
4. Nikki's height
5. Cammy's height

STEP 3

We don't have any numbers here, just the question "is the scale drawing larger than the actual spider?".
Scale drawings are usually bigger than the actual tiny things, so the drawing is probably larger.
Think about it – you wouldn't draw a spider smaller than it really is, that'd be hard to see!
So, yes, the scale drawing is larger.

STEP 4

The map shows $2.5$ centimeters for every $3$ miles in real life.
So the scale is $2.5$ cm : $3$ mi.
We can simplify this by dividing both sides by $2.5$ to get $1$ cm : $1.2$ mi.
So, every $1$ centimeter on the map represents $1.2$ miles in the real world.

STEP 5

The bedroom is $4$ inches wide on the blueprint, but $12$ yards wide in real life. Hold up! We need the same units.
There are $36$ inches in a yard, so the real bedroom is $12 \cdot 36 = 432$ inches wide.

STEP 6

Now we can compare: $4$ inches on the blueprint represents $432$ inches in real life.
The scale is $4$ in : $432$ in.
Divide both sides by $4$ to get $1$ in : $108$ in.
So every inch on the blueprint represents $108$ inches in the real house.

STEP 7

Jimmy is $6$ feet tall with a $10$ foot shadow.
Nikki has a $9$ foot shadow.
We can set up a proportion: $\frac{\text{Jimmy's height}}{\text{Jimmy's shadow}} = \frac{\text{Nikki's height}}{\text{Nikki's shadow}}$ .

STEP 8

Let $x$ be Nikki's height.
Plugging in the values, we get $\frac{6}{10} = \frac{x}{9}$ .

STEP 9

Solve for $x$ by multiplying both sides by $9$ : $x = \frac{6}{10} \cdot 9 = \frac{54}{10} = 5.4$ .
So, Nikki is $5.4$ feet tall!

STEP 10

The tree is $25$ feet tall with a $20$ foot shadow.
Cammy has a $5$ foot shadow.
We set up another proportion: $\frac{\text{Tree's height}}{\text{Tree's shadow}} = \frac{\text{Cammy's height}}{\text{Cammy's shadow}}$ .

STEP 11

Let $y$ be Cammy's height.
We get $\frac{25}{20} = \frac{y}{5}$ .

STEP 12

Solve for $y$ by multiplying both sides by $5$ : $y = \frac{25}{20} \cdot 5 = \frac{125}{20} = 6.25$ .
Cammy is $6.25$ feet tall!

STEP 13

The scale drawing is larger than the actual spider. The map scale is $1$ cm : $1.2$ mi. The blueprint scale is $1$ in : $108$ in. Nikki is $5.4$ feet tall. Cammy is $6.25$ feet tall.

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Studdy Solution

STEP 1

STEP 2

1. Spider size
2. Map scale
3. Blueprint scale
4. Nikki's height
5. Cammy's height

STEP 3

STEP 4

The map shows $2.5$ centimeters for every $3$ miles in real life.
So the scale is $2.5$ cm : $3$ mi.
We can simplify this by dividing both sides by $2.5$ to get $1$ cm : $1.2$ mi.
So, every $1$ centimeter on the map represents $1.2$ miles in the real world.

STEP 5

The bedroom is $4$ inches wide on the blueprint, but $12$ yards wide in real life. Hold up! We need the same units.
There are $36$ inches in a yard, so the real bedroom is $12 \cdot 36 = 432$ inches wide.

STEP 6

Now we can compare: $4$ inches on the blueprint represents $432$ inches in real life.
The scale is $4$ in : $432$ in.
Divide both sides by $4$ to get $1$ in : $108$ in.
So every inch on the blueprint represents $108$ inches in the real house.

STEP 7

Jimmy is $6$ feet tall with a $10$ foot shadow.
Nikki has a $9$ foot shadow.
We can set up a proportion: $\frac{\text{Jimmy's height}}{\text{Jimmy's shadow}} = \frac{\text{Nikki's height}}{\text{Nikki's shadow}}$ .

STEP 8

Let $x$ be Nikki's height.
Plugging in the values, we get $\frac{6}{10} = \frac{x}{9}$ .

STEP 9

Solve for $x$ by multiplying both sides by $9$ : $x = \frac{6}{10} \cdot 9 = \frac{54}{10} = 5.4$ .
So, Nikki is $5.4$ feet tall!

STEP 10

The tree is $25$ feet tall with a $20$ foot shadow.
Cammy has a $5$ foot shadow.
We set up another proportion: $\frac{\text{Tree's height}}{\text{Tree's shadow}} = \frac{\text{Cammy's height}}{\text{Cammy's shadow}}$ .

STEP 11

Let $y$ be Cammy's height.
We get $\frac{25}{20} = \frac{y}{5}$ .

STEP 12

Solve for $y$ by multiplying both sides by $5$ : $y = \frac{25}{20} \cdot 5 = \frac{125}{20} = 6.25$ .
Cammy is $6.25$ feet tall!

STEP 13

The scale drawing is larger than the actual spider. The map scale is $1$ cm : $1.2$ mi. The blueprint scale is $1$ in : $108$ in. Nikki is $5.4$ feet tall. Cammy is $6.25$ feet tall.

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Studdy Solution

STEP 1

STEP 2

1. Spider size2. Map scale3. Blueprint scale4. Nikki's height5. Cammy's height

STEP 3

STEP 4

The map shows 2.52.52.5 centimeters for every 333 miles in real life.So the scale is 2.52.52.5 cm : 333 mi.We can simplify this by dividing both sides by 2.52.52.5 to get 111 cm : 1.21.21.2 mi.So, every 111 centimeter on the map represents 1.21.21.2 miles in the real world.

STEP 5

The bedroom is 444 inches wide on the blueprint, but 121212 *yards* wide in real life. **Hold up!** We need the same units.There are 363636 inches in a yard, so the real bedroom is 12⋅36=43212 \cdot 36 = 43212⋅36=432 inches wide.

STEP 6

Now we can compare: 444 inches on the blueprint represents 432432432 inches in real life.The scale is 444 in : 432432432 in.Divide both sides by 444 to get 111 in : 108108108 in.So every inch on the blueprint represents 108108108 inches in the real house.

STEP 7

STEP 8

Let xxx be Nikki's height.Plugging in the values, we get 610=x9\frac{6}{10} = \frac{x}{9}106​=9x​.

STEP 9

**Solve for** xxx by multiplying both sides by 999: x=610⋅9=5410=5.4x = \frac{6}{10} \cdot 9 = \frac{54}{10} = 5.4x=106​⋅9=1054​=5.4.So, Nikki is 5.45.45.4 feet tall!

STEP 10

STEP 11

Let yyy be Cammy's height.We get 2520=y5\frac{25}{20} = \frac{y}{5}2025​=5y​.

STEP 12

**Solve for** yyy by multiplying both sides by 555: y=2520⋅5=12520=6.25y = \frac{25}{20} \cdot 5 = \frac{125}{20} = 6.25y=2025​⋅5=20125​=6.25.Cammy is 6.256.256.25 feet tall!

STEP 13

The scale drawing is larger than the actual spider. The map scale is 111 cm : 1.21.21.2 mi. The blueprint scale is 111 in : 108108108 in. Nikki is 5.45.45.4 feet tall. Cammy is 6.256.256.25 feet tall.

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1. Spider size
2. Map scale
3. Blueprint scale
4. Nikki's height
5. Cammy's height

The map shows $2.5$ centimeters for every $3$ miles in real life.
So the scale is $2.5$ cm : $3$ mi.
We can simplify this by dividing both sides by $2.5$ to get $1$ cm : $1.2$ mi.
So, every $1$ centimeter on the map represents $1.2$ miles in the real world.

The bedroom is $4$ inches wide on the blueprint, but $12$ yards wide in real life. Hold up! We need the same units.
There are $36$ inches in a yard, so the real bedroom is $12 \cdot 36 = 432$ inches wide.

Now we can compare: $4$ inches on the blueprint represents $432$ inches in real life.
The scale is $4$ in : $432$ in.
Divide both sides by $4$ to get $1$ in : $108$ in.
So every inch on the blueprint represents $108$ inches in the real house.

Let $x$ be Nikki's height.
Plugging in the values, we get $\frac{6}{10} = \frac{x}{9}$ .

Solve for $x$ by multiplying both sides by $9$ : $x = \frac{6}{10} \cdot 9 = \frac{54}{10} = 5.4$ .
So, Nikki is $5.4$ feet tall!

Let $y$ be Cammy's height.
We get $\frac{25}{20} = \frac{y}{5}$ .

Solve for $y$ by multiplying both sides by $5$ : $y = \frac{25}{20} \cdot 5 = \frac{125}{20} = 6.25$ .
Cammy is $6.25$ feet tall!

The scale drawing is larger than the actual spider. The map scale is $1$ cm : $1.2$ mi. The blueprint scale is $1$ in : $108$ in. Nikki is $5.4$ feet tall. Cammy is $6.25$ feet tall.