Question

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?

Answer 1

No. of marbles with Erick at first = 45

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

Answer 2

45

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