Answer to Question #23809 in Abstract Algebra for Amilyah

Question

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

Answer 1

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.