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If y varies directly as x, and y=20 when x=6, find x when y=15. with solution

Sagot :

NataleighScottlynidn

Problem:

If y varies directly as x, and y = 20 when x = 6, find x when y = 15.

Solution:

A direct variation is a relationship between two variables, x and y, that can be written as y = kx where k ≠ 0.

The statement, "y varies directly as x" translated into directly variation is y = kx where k is the constant of variation.

Solve if y is 20 and x is 6. So, find the constant using the equation of a combined variation.

  • y = kx
  • (20) = k(6)
  • 20 = 6k
  • 6k/6 = 20/6
  • k = 10/3

The constant of the variation is 10/3. In equation of variation.

  • y = 10/3x

Find x when y is 15. Substitute the equation using the constant of the variation that you obtained.

  • y = 10/3x
  • (15) = 10/3x
  • 15 × 3/10 = x
  • x = 9/5 or 4.5

Answer:

∴ Therefore, the value of x is 9/5 or 4.5 to the directly variation.

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