Question

module 7 pretest: rational expressions and equations
score: 8/9 answered: 8/9
question 9
when 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 950 usd can be converted into 31,079.25 php.

find the constant of proportionality k.
k = \boxed{} (if needed, round answer to 3 decimal places.)

using the k from above find the amout of php given that you have 1,400 usd to convert.
you will receive \boxed{} php (if needed, round answer to 2 decimal places.)

enter dne for does not exist, oo for infinity

Explanation:

Step1: Define direct proportionality

Let \( y \) be the amount of PHP and \( x \) be the amount of USD. Since they are directly proportional, \( y = kx \), where \( k \) is the constant of proportionality.

Step2: Find \( k \) using given values

We know \( x = 950 \) USD and \( y = 31079.25 \) PHP. Substitute into \( y = kx \): \( 31079.25 = k \times 950 \). Solve for \( k \): \( k=\frac{31079.25}{950} \).

Step3: Calculate \( k \)

\( k=\frac{31079.25}{950}=32.715 \) (exact value, no rounding needed here as it's a clean division).

Step4: Find PHP for 1400 USD

Now use \( y = kx \) with \( x = 1400 \) and \( k = 32.715 \). So \( y = 32.715\times1400 \).

Step5: Calculate \( y \)

\( 32.715\times1400 = 45801.00 \) (since \( 32.715\times1400 = 32.715\times1000+32.715\times400 = 32715+13086 = 45801 \)).

Answer:

For the constant of proportionality \( k \): \( k = 32.715 \)
For the amount of PHP with 1400 USD: \( 45801.00 \)