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 1,150 USD can be converted into 64,074.55 PHP. Find the constant of proportionality k k= (If needed, round answer to 3 decimal places ) Using the k from above find the amout of PHP given that you have 1,350 USD to convert: you will receive PHP (If needed, round answer to 2 decimal places ) Enter DNE for Does Not Exist; oo for Infinity
The Correct Answer and Explanation is:
To solve this, we can use the concept of direct proportionality, which means that the amount of Philippine Pesos (PHP) received is directly proportional to the amount of US Dollars (USD) exchanged.
Step 1: Find the constant of proportionality (k)
The equation for direct proportionality is:PHP=k×USD\text{PHP} = k \times \text{USD}PHP=k×USD
Given that 1,150 USD can be converted into 64,074.55 PHP, we can solve for the constant of proportionality kkk:64,074.55=k×1,15064,074.55 = k \times 1,15064,074.55=k×1,150k=64,074.551,150=55.7k = \frac{64,074.55}{1,150} = 55.7k=1,15064,074.55=55.7
Thus, the constant of proportionality kkk is 55.7 (rounded to three decimal places).
Step 2: Find the amount of PHP for 1,350 USD
Now that we know k=55.7k = 55.7k=55.7, we can use the formula to find the amount of PHP that 1,350 USD will convert into:PHP=55.7×1,350=75,195.0\text{PHP} = 55.7 \times 1,350 = 75,195.0PHP=55.7×1,350=75,195.0
Thus, for 1,350 USD, you will receive 75,195.00 PHP (rounded to two decimal places).
Final Answers:
- The constant of proportionality k=55.7k = 55.7k=55.7
- For 1,350 USD, you will receive 75,195.00 PHP.
