Question

Kate and Nora each have a sum of money. 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. Find the sum
of money Kate had initially​

Answer 1

Let Kate has x and Nora has y

sum of money

Now, According to Question

35=xy

⇒y=53x

After Nora gives Kate Rs.

150

79=x+150−150

⇒7y−1050=9x+1350

⇒7y−9x=2400

⇒7×53x-9x=2400

⇒x=900

So, Kate had Rs.

900 initially

Answer 2

Answer:

Let Kate has x

and Nora has y sum of money

Now, According to Question

$\huge{ \color{lime} \frac35 \implies\frac xy \implies y= \frac 53x}$

After Nora gives Kate Rs.150

$\small \color{lime}{\frac 79 \: \: \: . \: \: \: \: \frac{x + 150}{y - 150} \implies \: \: 7y−1050 = 9x+1350⇒7y−9x=2400⇒7× \frac{5}{3}x−9x=2400⇒x=900</p><p></p><p></p><p>}$

x−9x=2400⇒x=900

So, Kate had Rs.900

Step-by-step explanation:

thx