Answer:
1. [tex]xy = 63[/tex]
2. [tex]y = 3[/tex]
Step-by-step explanation:
Given
Variation: inverse Proportion
y = 7, x = 9
Required
- Write an equation connecting y and x
- Find y when x = 21
Given that thee variation is inversely proportional;
This implies that
[tex]y\ \alpha\ \frac{1}{x}[/tex]
Convert variation to equation
[tex]y\ = \frac{k}{x}[/tex] ----------- Equation 1
Where k is the constant of variation
Substitute 7 for y and 9 for x in equation 1
[tex]7 = \frac{k}{9}[/tex]
Multiply both sides by 9
[tex]9 * 7 = 9 * \frac{k}{9}[/tex]
[tex]63 = k[/tex]
Substitute 63 for k in equation 1
[tex]y = \frac{63}{x}[/tex]
Multiply both sides by x
[tex]x * y = \frac{63}{x} * x[/tex]
[tex]xy = 63[/tex]
Hence, the equation connecting x and y is [tex]xy = 63[/tex]
Solving for when x = 21
Substitute 21 for x in the above equation
[tex]21 * y = 63[/tex]
Divide both sides by 21
[tex]\frac{21 * y}{21} = \frac{63}{21}[/tex]
[tex]y = 3[/tex]
