Question #8333d

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Question #8333d

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Answer 1 · 2017-03-13T21:02:21

$x = 2$ $x = 2$

Explanation:

Varies directly means that it is proportional: $A = k B$ $A = kB$ where $k$ $k$ is the constant of proportionality.

$x = k y$ $x = ky$

Solve for $k$ $k$ :

$8 = k \cdot 24$ $8 = k * 24$ so $k = \frac{8}{24} = \frac{1}{3}$ $k = 8/24 = 1/3$

So when $y = 6$ $y = 6$ : $x = \frac{1}{3} \cdot 6 = 2$ $x = 1/3 * 6 = 2$

You can also solve this problem using proportions without a $k$ $k$ :
$\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}$ $x_1/y_1 = x_2/y_2$ ; $\frac{8}{24} = \frac{x_{2}}{6}$ $8/24 = x_2/6$

Using the cross product $x_{1} \cdot y_{2} = x_{2} \cdot y_{1}$ $x_1 * y_2 = x_2* y_1$

$24 x_{2} = 48$ $24x_2 = 48$

So $x_{2} = \frac{48}{24} = 2$ $x_2 = 48/24 = 2$

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Question #8333d

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