Question

One of these scenarios represents a direct variation and one does not. How can you tell the difference? a) A large pizza with one topping costs $15.50. A large pizza with 4 toppings costs $20. Does the price vary directly with the number of toppings? b) A marathoner ran 5 miles in 40 minutes and 15 miles in 120 minutes. Does the number of minutes vary directly with the number of miles? Your answer:

Answer 1

Answer: See explanation

Step-by-step explanation:

a) A large pizza with one topping costs $15.50. A large pizza with 4 toppings costs $20.

A large pizza with one topping costs $15.50.

Using the formula for direct variation,

y = kx

where,

y = Cost of pizza

x = number of toppings

k = constant of proportionality

15.50 = 1k

k = 15.50

A large pizza with 4 toppings costs $20.

Using y = kx

20 = 4k

k = 20/4

k = 5

Here, the price does not vary directly with the number of toppings because the constant of proportionality is different.

b) A marathoner ran 5 miles in 40 minutes and 15 miles in 120 minutes.

Using y = kx

where,

y = 40

x = 5

y = kx

40 = 5k

k = 40/5

k = 8

Using y = kx

where,

y = 120

x = 15

y = kx

120 = 15k

k = 120/15

k = 8

The number of minutes vary directly with the number of miles. This is because the constant of proportionality is thesame in both cases.

Therefore, the second one(B) represents a direct variation and the first one (A) doesn't.