If x varies directly as y and x=42 and y=6, What is the value of y when x=21?. Created by athena196. Math

DIRECT VARIATIONIf x varies directly as y and x=42 and y=6, What is the value of y when x=21?Solution 1 :Since x varies directly as y , then the equation of variation is in the form Substitute the given values of x and y to solve for k in the equation.Solving for y when x=21Solution 2 : We have:Variation EquationConstant of VariationFinal Answer

If x varies directly as y and x=42 and y=6, What is the value of y when x=21?...

aliyah1732

DIRECT VARIATION

If x varies directly as y and x=42 and y=6, What is the value of y when x=21?

Solution 1 :

Since x varies directly as y , then the equation of variation is in the form $\tt{x = ky.}$

Substitute the given values of x and y to solve for k in the equation.

$\tt{x = ky} \\ \tt{42 = 6k} \\ \tt{\frac{42}{6} = \frac{6k}{6}} \\ \sf{7 = k \: \: or \: \: k = 7}$

$\sf{Hence, \: the \: equation \: of \: variation \: is \: \: x=7y}$

Solving for y when x=21

$\tt{x = 7y} \\ \tt{21 = 7y} \\ \ \tt{\frac{21}{7} = \frac{7y}{7}} \\ \sf{3 = y \: \: \: or \: \: \: y = 3}$

$\sf{Therefore, \: the \: solution is \: \: y=3.}$

Solution 2 :

$\sf{Since \: \: \frac{x}{y} \: \: is \: a \: constant,then \: we \: can \: write \: k = \frac{x}{y} .}$ $\sf{From \: here,we \: can \: establish \: a \: proportion \: such \: that \: \frac{ x_{1}}{ y_{1} } = \frac{ x_{2} }{ y_{2} } \: where \: x_{1} = 42 }, y_{1} = 6 \: and \: x_{2} = 21$

We have:

$\tt{\frac{ x_{1}}{ y_{1}} = \frac{ x_{2} }{ y_{2}} } \\ \tt{\frac{42}{6} = \frac{21}{ y_{2}} } \\ \tt{7 = \frac{21}{ y_{2}} } \\ \tt{7 y_{2} = 21} \\ \tt{\frac{7 y_{2} }{7} = \frac{21}{7}} \\ \tt{y_{2} = 3}$