# Answer to Question #23809 in Abstract Algebra for Amilyah

Question #23809

Xuxian and Rachel had the same number of marbles. After Rachel gave away 10 marbles and Xuxian gave away 22 marbles, Rachel had 3 times as many marble as Xuxian. How many marbles did each of them have at first

Expert's answer

Let Xuxian and Rachel had X and R marbles first time. Then we can write down the system of equations:

X = R,

R - 10 = 3(X - 22).

Let's solve it. Substituting the first equation into the second one we obtain:

R - 10 = 3(R - 22) ==>

R - 10 = 3R - 66 ==>

56 = 2R ==>

R = 28.

Therefore, Xuxian and Rachel had 28 marbles each.

X = R,

R - 10 = 3(X - 22).

Let's solve it. Substituting the first equation into the second one we obtain:

R - 10 = 3(R - 22) ==>

R - 10 = 3R - 66 ==>

56 = 2R ==>

R = 28.

Therefore, Xuxian and Rachel had 28 marbles each.

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