Question

Alice and bernice had some money in the ratio 7:3. After alice Had given BErnice some money, the ratio of the amount of money alice had to the amount of money BErnice had became 7:13. Bernice had $204 more than alice in the end. How much money did alice give bernice

Answer 1

Answer:

Alice gave $238 to Bernice.

Step-by-step explanation:

Let the amount of Alice has be 7x.

Let the amount of Bernice has be 3x.

Let the amount given to Bernice be y

Amount left with Alice = 7x-y

Amount left with Bernice = 3x+y

After giving some amount Bernice, ratio of money left with Alice to Bernice  : 7 :13

$\frac{7x-y}{3x+y}=\frac{7}{13}$

$13(7x-y)=7(3x+y)$

91x-13y=21x+7y

70x=20y

$x=\frac{2y}{7}$..[1]

Bernice had $204 more than Alice in the end.

(3x+y)-(7x-y) = 204

-4x + 2y = 204

-2x + y = 102..[2]

Using value of x from [1] in [2] :

$-2\frac{2y}{7}+y=102$

$\frac{3y}{7}=102$

$y=\frac{102\times 7}{3}=238$

y = $238

Alice gave $238 to Bernice.