Question

Rachel and Sean had the same number of marbles. Rachel gave away 20 marbles and Sean gave away 44 marbles. Rachel then had 3 times as many marbles as Sean. How many marbles did Rachel and Sean each have at first?​

Answer 1

r - 20 = 3(r - 44)

r - 20 = 3r - 132

2r = 112

r = 56

Rachel and Sean each had 56 marbles at first.

Rachel: 56 - 20 = 36 marbles left

Sean: 56 - 44 = 12 marbles left

Answer 2

Rachel and Sean each had 56 marbles at first.

Explanation:

Let x be the number of marbles Rachel and Sean had at first.

Rachel had x - 20 marbles after giving away 20 marbles.

Sean had x - 44 marbles after giving away 44 marbles.

So,

`\sf x - 20 = 3(x - 44)`

Opening bracket on the right side:

`\sf x-20=3x-132`

Adding both side by 132.

`\sf x-20+132 =3x-132+132`

`\sf x +112 =3x`

Subtracting x on both sides.

`\sf x +112 -x =3x-x`

`\sf 112=2x`

Dividing both sides by 2:

`\sf (112)/(2)= (2x)/(2)`

`\sf 56 = x`

So,

`\sf x = 56`

Therefore, Rachel and Sean each had 56 marbles at first.