Respuesta :
Given:
The ratio of the amount of money Kate has to that of Nora is 3 : 5.
After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.
To find:
The sum of money Kate had initially.
Solution:
Let the initial amount of money Kate and Nora have are 3x and 5x respectively.
After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.
The amount of Kate = 3x+150
The amount of Nora = 5x-150
Now,
[tex]\dfrac{3x+150}{5x-150}=\dfrac{7}{9}[/tex]
[tex]9(3x+150)=7(5x-150)[/tex]
[tex]27x+1350=35x-1050[/tex]
[tex]1350+1050=35x-27x[/tex]
[tex]2400=8x[/tex]
Divide both sides by 8.
[tex]300=x[/tex]
Putting x=300 in 3x, to get the amount of money Kate has initially.
[tex]3(300)=900[/tex]
Therefore, the Kate initially had $900.
