Question

1. Given that y and x are directly proportional and y=2 when x=5, find the value of y when x=15.

2. The number of gallons of fuel used in a trip varies directly with the number of miles traveled. If a trip of 270 miles required 12 gallons of fuel, how many gallons are required for a trip of 400 miles?
3. Karen earns 285 pesos for working six hours. If the amount she earned varies directly with the number of hours she works, how much will she earn if she works 10 hours?
4. A 150-ml bottle of food coloring costs 5.25 pesos. If the cost varies directly with the volume of juice, what should be the cost of a 250-ml bottle of food coloring?
5. An egg is dropped from the rooftop. The distance it falls varies directly with the square of the time it falls. It takes 0.5 seconds for the egg to fall 8 feet. How long will it take the egg to fall from the height of 200 feet?

Answer 1

To find the value of y when x is 15 and knowing y and x are directly proportional and y=2 when x=5, we first determine the constant of proportionality (k=0.4) and then use it to calculate y=6 when x=15.

Step-by-step explanation:

When dealing with directly proportional relationships, we can say that y is directly proportional to x, or y = kx, where k is the proportionality constant. To find the value of y when x is 15, we first need to determine the constant of proportionality using the information that y=2 when x=5.

By substituting the given values into the proportionality equation, we get:
2 = k * 5. From this, we can solve for k:
k = 2 / 5, which gives us k = 0.4.

Now that we have the proportionality constant, we can find the value of y when x is 15 by using the equation y = kx:
y = 0.4 * 15. Thus,
y = 6. The value of y when x is 15 is 6.