If x varies directly with y, and x is 25 when y is 10, what is the value of x when y is 16, 15, 8, and 75?

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To solve the problem, we start with the direct variation relationship where x varies directly with y, which can be expressed mathematically as:

x = k * y

where k is the constant of proportionality. Given the information that x is 25 when y is 10, we can substitute these values into the equation to find k:

  • x = 25, y = 10

Substituting these values:

25 = k * 10

To find k, we divide both sides by 10:

k = 25 / 10 = 2.5

Now that we have our constant k, we can find the values of x for y = 16, 15, 8, and 75.

Finding x for different values of y:

  • When y = 16:

x = 2.5 * 16 = 40

  • When y = 15:

x = 2.5 * 15 = 37.5

  • When y = 8:

x = 2.5 * 8 = 20

  • When y = 75:

x = 2.5 * 75 = 187.5

Summary:

  • If y = 16, then x = 40
  • If y = 15, then x = 37.5
  • If y = 8, then x = 20
  • If y = 75, then x = 187.5

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