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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .