Question Given directly proportional ratios, find the missing variable $y_2$ if $x_1=500$ , $y_1=250$ , and $x_2=370$ .

Studdy Solution

STEP 1

Assumptions
1. The ratios $x_1:y_1$ and $x_2:y_2$ are directly proportional.
2. The given values are $x_1 = 500$ , $y_1 = 250$ , and $x_2 = 370$ .
3. We need to find the value of $y_2$ .

STEP 2

Since the ratios are directly proportional, we can write the proportionality as:
$\frac{x_1}{y_1} = \frac{x_2}{y_2}$

STEP 3

Now, plug in the given values for $x_1$ , $y_1$ , and $x_2$ to solve for $y_2$ .
$\frac{500}{250} = \frac{370}{y_2}$

STEP 4

Simplify the left side of the equation.
$\frac{500}{250} = 2$

STEP 5

Now the equation is:
$2 = \frac{370}{y_2}$

STEP 6

To solve for $y_2$ , we can cross-multiply.
$2 \cdot y_2 = 370$

STEP 7

Divide both sides of the equation by 2 to isolate $y_2$ .
$y_2 = \frac{370}{2}$

STEP 8

Calculate the value of $y_2$ .
$y_2 = 185$
The value of $y_2$ is 185.

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Question Given directly proportional ratios, find the missing variable $y_2$ if $x_1=500$ , $y_1=250$ , and $x_2=370$ .

Studdy Solution

STEP 1

Assumptions
1. The ratios $x_1:y_1$ and $x_2:y_2$ are directly proportional.
2. The given values are $x_1 = 500$ , $y_1 = 250$ , and $x_2 = 370$ .
3. We need to find the value of $y_2$ .

STEP 2

Since the ratios are directly proportional, we can write the proportionality as:
$\frac{x_1}{y_1} = \frac{x_2}{y_2}$

STEP 3

Now, plug in the given values for $x_1$ , $y_1$ , and $x_2$ to solve for $y_2$ .
$\frac{500}{250} = \frac{370}{y_2}$

STEP 4

Simplify the left side of the equation.
$\frac{500}{250} = 2$

STEP 5

Now the equation is:
$2 = \frac{370}{y_2}$

STEP 6

To solve for $y_2$ , we can cross-multiply.
$2 \cdot y_2 = 370$

STEP 7

Divide both sides of the equation by 2 to isolate $y_2$ .
$y_2 = \frac{370}{2}$

STEP 8

Calculate the value of $y_2$ .
$y_2 = 185$
The value of $y_2$ is 185.

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Question Given directly proportional ratios, find the missing variable y2y_2y2​ if x1=500x_1=500x1​=500, y1=250y_1=250y1​=250, and x2=370x_2=370x2​=370.

Studdy Solution

STEP 1

Assumptions1. The ratios x1:y1x_1:y_1x1​:y1​ and x2:y2x_2:y_2x2​:y2​ are directly proportional.2. The given values are x1=500x_1 = 500x1​=500, y1=250y_1 = 250y1​=250, and x2=370x_2 = 370x2​=370.3. We need to find the value of y2y_2y2​.

STEP 2

Since the ratios are directly proportional, we can write the proportionality as:x1y1=x2y2\frac{x_1}{y_1} = \frac{x_2}{y_2}y1​x1​​=y2​x2​​

STEP 3

Now, plug in the given values for x1x_1x1​, y1y_1y1​, and x2x_2x2​ to solve for y2y_2y2​.500250=370y2\frac{500}{250} = \frac{370}{y_2}250500​=y2​370​

STEP 4

Simplify the left side of the equation.500250=2\frac{500}{250} = 2250500​=2

STEP 5

Now the equation is:2=370y22 = \frac{370}{y_2}2=y2​370​

STEP 6

To solve for y2y_2y2​, we can cross-multiply.2⋅y2=3702 \cdot y_2 = 3702⋅y2​=370

STEP 7

Divide both sides of the equation by 2 to isolate y2y_2y2​.y2=3702y_2 = \frac{370}{2}y2​=2370​

STEP 8

Calculate the value of y2y_2y2​.y2=185y_2 = 185y2​=185The value of y2y_2y2​ is 185.

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Question Given directly proportional ratios, find the missing variable $y_2$ if $x_1=500$ , $y_1=250$ , and $x_2=370$ .

Assumptions
1. The ratios $x_1:y_1$ and $x_2:y_2$ are directly proportional.
2. The given values are $x_1 = 500$ , $y_1 = 250$ , and $x_2 = 370$ .
3. We need to find the value of $y_2$ .

Since the ratios are directly proportional, we can write the proportionality as:
$\frac{x_1}{y_1} = \frac{x_2}{y_2}$

Now, plug in the given values for $x_1$ , $y_1$ , and $x_2$ to solve for $y_2$ .
$\frac{500}{250} = \frac{370}{y_2}$

Simplify the left side of the equation.
$\frac{500}{250} = 2$

Now the equation is:
$2 = \frac{370}{y_2}$

To solve for $y_2$ , we can cross-multiply.
$2 \cdot y_2 = 370$

Divide both sides of the equation by 2 to isolate $y_2$ .
$y_2 = \frac{370}{2}$

Calculate the value of $y_2$ .
$y_2 = 185$
The value of $y_2$ is 185.