Math / Algebra

QuestionGot II? 3. The length of the ball court at La Venta is 14 times the height of its walls. Write an equation that can be used to find the height of a model that has a length of 49 cm .

Studdy Solution

STEP 1

What is this asking? We need to figure out how tall a model of the La Venta ball court should be if it's 49 cm long and the real court is 14 times longer than it is tall. Watch out! Don't mix up the length and the height!
We're given the length of the model and need to find the height.

STEP 2

1. Set up the relationship
2. Solve for the height

STEP 3

Let's use $L$ for the length of the model and $H$ for the height of the model.
We're told that the length is 14 times the height.

STEP 4

So, we can write this relationship as $L = 14 \cdot H$ .
This equation tells us that whatever the height is, the length is 14 times bigger!

STEP 5

We know the model's length is 49 cm, so we can substitute $\textbf{49}$ for $L$ in our equation: $49 = 14 \cdot H$ .

STEP 6

Now, we want to get $H$ all by itself.
Since $H$ is being multiplied by 14, we can divide both sides of the equation by 14 to isolate $H$ .
Remember, what we do to one side, we must do to the other to keep the equation balanced!

STEP 7

$\frac{49}{14} = \frac{14 \cdot H}{14}$ We divide to one on the right side, leaving just $H$ .
On the left, $49$ divided by $14$ is $\textbf{3.5}$ .
So, $3.5 = H$ .

STEP 8

The height of the model should be 3.5 cm.

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QuestionGot II? 3. The length of the ball court at La Venta is 14 times the height of its walls. Write an equation that can be used to find the height of a model that has a length of 49 cm .

Studdy Solution

STEP 1

What is this asking? We need to figure out how tall a model of the La Venta ball court should be if it's 49 cm long and the real court is 14 times longer than it is tall. Watch out! Don't mix up the length and the height!
We're given the length of the model and need to find the height.

STEP 2

1. Set up the relationship
2. Solve for the height

STEP 3

Let's use $L$ for the length of the model and $H$ for the height of the model.
We're told that the length is 14 times the height.

STEP 4

So, we can write this relationship as $L = 14 \cdot H$ .
This equation tells us that whatever the height is, the length is 14 times bigger!

STEP 5

We know the model's length is 49 cm, so we can substitute $\textbf{49}$ for $L$ in our equation: $49 = 14 \cdot H$ .

STEP 6

Now, we want to get $H$ all by itself.
Since $H$ is being multiplied by 14, we can divide both sides of the equation by 14 to isolate $H$ .
Remember, what we do to one side, we must do to the other to keep the equation balanced!

STEP 7

$\frac{49}{14} = \frac{14 \cdot H}{14}$ We divide to one on the right side, leaving just $H$ .
On the left, $49$ divided by $14$ is $\textbf{3.5}$ .
So, $3.5 = H$ .

STEP 8

The height of the model should be 3.5 cm.

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QuestionGot II? 3. The length of the ball court at La Venta is 14 times the height of its walls. Write an equation that can be used to find the height of a model that has a length of 49 cm .

Studdy Solution

STEP 1

What is this asking? We need to figure out how tall a model of the La Venta ball court should be if it's 49 cm long and the real court is 14 times longer than it is tall. Watch out! Don't mix up the length and the height!We're given the **length** of the model and need to find the **height**.

STEP 2

1. Set up the relationship2. Solve for the height

STEP 3

Let's use LLL for the length of the model and HHH for the height of the model.We're told that the length is **14 times** the height.

STEP 4

So, we can write this relationship as L=14⋅HL = 14 \cdot HL=14⋅H.This equation tells us that whatever the height is, the length is 14 times bigger!

STEP 5

We know the model's length is 49 cm, so we can **substitute** 49\textbf{49}49 for LLL in our equation: 49=14⋅H49 = 14 \cdot H49=14⋅H.

STEP 6

Now, we want to get HHH all by itself.Since HHH is being multiplied by 14, we can **divide both sides** of the equation by **14** to isolate HHH.Remember, what we do to one side, we *must* do to the other to keep the equation balanced!

STEP 7

4914=14⋅H14\frac{49}{14} = \frac{14 \cdot H}{14}1449​=1414⋅H​ We divide to one on the right side, leaving just HHH.On the left, 494949 divided by 141414 is 3.5\textbf{3.5}3.5.So, 3.5=H3.5 = H3.5=H.

STEP 8

The height of the model should be **3.5 cm**.

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? We need to figure out how tall a model of the La Venta ball court should be if it's 49 cm long and the real court is 14 times longer than it is tall. Watch out! Don't mix up the length and the height!
We're given the length of the model and need to find the height.

1. Set up the relationship
2. Solve for the height

Let's use $L$ for the length of the model and $H$ for the height of the model.
We're told that the length is 14 times the height.

So, we can write this relationship as $L = 14 \cdot H$ .
This equation tells us that whatever the height is, the length is 14 times bigger!

We know the model's length is 49 cm, so we can substitute $\textbf{49}$ for $L$ in our equation: $49 = 14 \cdot H$ .

Now, we want to get $H$ all by itself.
Since $H$ is being multiplied by 14, we can divide both sides of the equation by 14 to isolate $H$ .
Remember, what we do to one side, we must do to the other to keep the equation balanced!

$\frac{49}{14} = \frac{14 \cdot H}{14}$ We divide to one on the right side, leaving just $H$ .
On the left, $49$ divided by $14$ is $\textbf{3.5}$ .
So, $3.5 = H$ .

The height of the model should be 3.5 cm.