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Georgia [21]
2 years ago
9

When y is 4, p is 0. 5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equatio

n models the situation?
x p m y = 8
StartFraction x y Over p m EndFraction = 8
StartFraction x p m Over y EndFraction = 0. 5
StartFraction x Over p m y EndFraction = 0. 5
Mathematics
1 answer:
dmitriy555 [2]2 years ago
5 0

Answer:

  \dfrac{xy}{pm}=8

Step-by-step explanation:

If x varies directly as the product of p and m, and inversely with y, the relation can be written ...

  x = k(pm)/y . . . . where k is the constant of proportionality

__

This can be solved for k:

  k = xy/pm

For the given values, the value of k is ...

  k = (2)(4)/((0.5)(2)) = 8

Then the relation between the variables can be written ...

  (xy)/(pm) = 8

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Step-by-step explanation:

The coefficients of x and y do not have any "nice" relations, so doing this by elimination is just "brute force" with no particular subtlety.

After multiplying by appropriate numbers, you want the coefficient of one of the variables in one equation to be the opposite of the coefficient of the same variable in the other equation. Here, we can get that by multiplying the first equation by 7 and the second equation by 2.

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<em>Additional comment</em>

The multipliers used in this process are essentially the coefficients of one of the variables, with one of them negated. Here, we chose the x-coefficients, because negating one of them gives two positive multipliers. We judge it easier to do the arithmetic using positive numbers.

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