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

Step-by-step explanation:

Let the initial sum of money that Kate has be x Rs.

and let the initial sum of money that Nora has be y Rs.

The ratio of the amount of money Kate has to that of Nora is 3:5. Therefore, we have

x/y = 3/5

so, X = 3y/5

Now, Nora gives Rs. 150 to Kate.

so, the modified amount of money that Nora has is y - 150 Rs.

And the modified amount of money Kate has is x + 150 Rs.

After Nora gives Rs 150 to Kate the ratio amount of money Kate has to that of Nora become 7:9.

Therefore, The new ratio gives us x + 150/y - 150 = 7/9.

simplifying this equation we get,

9(x + 150) = 7(y - 150)

=> 9x + 1350 = 7y - 1050

=> 9x - 7y = -2400

subtracting x = 3y/5 in the above equation we get, 9(3y/5) - 7y = -2400

we will simplify the above equation,

27y/5 - 7y = -2400

=> 27y - 35y/ 5 = -2400

=> -8y = -2400 × 5

solving for y, we get

y = -2400 × 5/ -8

y = 300 × 5

y = 1500

we know that x = 3y/5 . subtracting y = 1500 in this equation, we will get the value of x,

x = 3 × 1500/5

=> x = 3 × 300

=> x = 900

Hence, the sum of money that Kate had intially was Rs. 900.