QuestionWhen exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received is directly proportional to the number of US Dollars to be exchanged. If 750 USD car be converted into $25,113.75$ PHP.
Find the constant of proportionality k . $\mathrm{k}=30,136.50 \quad \text { (If needed, round answer to } 3 \text { decimal places.) }$

Studdy Solution

STEP 1

1. The relationship between US Dollars (USD) and Philippine Pesos (PHP) is directly proportional.
2. 750 USD can be converted into 25,113.75 PHP.
3. We are tasked with finding the constant of proportionality, $k$ .

STEP 2

1. Understand the concept of direct proportionality.
2. Set up the equation for direct proportionality.
3. Solve for the constant of proportionality, $k$ .

STEP 3

Understand the concept of direct proportionality.
In direct proportionality, if $y$ is directly proportional to $x$ , then $y = kx$ , where $k$ is the constant of proportionality.

STEP 4

Set up the equation for direct proportionality.
Given that the number of Philippine Pesos (PHP) is directly proportional to the number of US Dollars (USD), we can write:
$\text{PHP} = k \times \text{USD}$
Substitute the given values into the equation:
$25,113.75 = k \times 750$

STEP 5

Solve for the constant of proportionality, $k$ .
Divide both sides of the equation by 750 to isolate $k$ :
$k = \frac{25,113.75}{750}$
Calculate the value:
$k = 33.485$
The constant of proportionality, rounded to three decimal places, is:
$\boxed{33.485}$

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