Respuesta :
Given:
Two equations are
[tex]\dfrac{50}{x}=\dfrac{10}{20}[/tex]
[tex]\dfrac{10}{50}=\dfrac{20}{x}[/tex]
To find:
The reason for same solutions to the proportions.
Solution:
First equation is
[tex]\dfrac{50}{x}=\dfrac{10}{20}[/tex]
On cross multiplication, we get
[tex]50\times 20=10\times x[/tex]
[tex]1000=10x[/tex]
Divide both sides by 10.
[tex]\dfrac{1000}{10}=x[/tex]
[tex]100=x[/tex]
The second equation is
[tex]\dfrac{10}{50}=\dfrac{20}{x}[/tex]
On cross multiplication, we get
[tex]10\times x=50\times 20[/tex]
[tex]10x=1000[/tex]
Divide both sides by 10.
[tex]x=\dfrac{1000}{10}[/tex]
[tex]x=100[/tex]
Solutions to the proportions are same because both result in the equation 10 x = 1,000, which simplifies to x = 100.
Therefore, the correct option is D.
