The ratio of erick's marbles to henry's marbles was 3: 2. after erick lost 15 marbles to henry, the ratio became 2: 3. how many marbles did erick have at first?

45

Step-by-step explanation:

Erick: x

Henry: y

X:y=3:2

(x-15):(y+15)=2:3

2x=3y ….①

3x-45=2y+30

3x=2y+75 …②

① * 3…  6x=9y

② * 2 … 6x=4y+150

9y=4y+150

5y=150

Y=30

X=45

No. of marbles with Erick at first =  45

Step-by-step explanation:

ratio of Erick's marbles to Henry's marbles =  3:2

No.of marbles with Erick = 3x

No. of marbles with Henry = 2x

Erick lost 15 marbles to Henry.

So, now the no. of marbles with Erick = 3x - 15

now the no. of marbles with Henry = 2x + 15

3x - 15 / 2x+15 = 2/3

3 *( 3x -15) = 2 * ( 2x +15)                  {cross multiplication}

3*3x - 3*15 = 2*2x + 2*15

9x - 45   = 4x + 30

9x - 4x = 30 + 45

         5x = 75

           x = 75/5

           x = 15

No. of marbles with Erick at first = 3x = 3*15 = 45