Joyce and Eunice each have some seashells. If Joyce gives 36 seashells to Eunice, both of them will have the same number of seashells. I Eunice gives 12 seashells to Joyce, the number of seashells that Joyce has to the number of seashells Eunice has will be in the ration of 5:1. How many seashells does each girl have?

Question

Joyce and Eunice each have some seashells. If Joyce gives 36 seashells to Eunice, both of them will have the same number of seashells. I Eunice gives 12 seashells to Joyce, the number of seashells that Joyce has to the number of seashells Eunice has will be in the ration of 5:1. How many seashells does each girl have?

Answer 1

Let J be the number of seashells Joyce has and E be the number of seashells Eunice has.

If Joyce gives 36 seashells to Eunice, both of them will have the same number of seashells, meaning J - 36 = E + 36.
If Eunice gives 12 seashells to Joyce, the number of seashells that Joyce has to the number of seashells Eunice has will be in the ration 5:1, meaning (J + 12)/(E - 12) = 5/1.
We know that J - 36 = E + 36, so let's substitute J with E + 72: (E + 72 + 12)/(E - 12) = 5/1
(E + 84)/(E - 12) = 5/1
5(E-12) = E + 84
5E - 60 = E + 84
4E = 144
E = <<36=36>>36
Eunice has 36 seashells
Since J - 36 = E + 36, J = E + 36 + 36 = 36 + 36 = <<36+36=72>>72
Joyce has 72 seashells. Answer: \boxed{36, 72}.

Answer 2

Let's assume that Joyce has J seashells and Eunice has E seashells.

According to the given information, if Joyce gives 36 seashells to Eunice, then both of them will have the same number of seashells. So, after Joyce gives 36 seashells, Joyce will have J - 36 seashells and Eunice will have E + 36 seashells.

Now, if Eunice gives 12 seashells to Joyce, then the ratio of the number of seashells Joyce has to the number of seashells Eunice has will be 5:1. So, the equation is:

(J - 36) / (E + 36) = 5/1

Cross multiplying:

1 * (J - 36) = 5 * (E + 36)
J - 36 = 5E + 180

Simplifying the equation:

J - 5E = 216 ----(1)

From the first condition, we know that after Joyce gives 36 seashells, both of them will have the same number of seashells. So,

J - 36 = E + 36
J - E = 72 ----(2)

Using equation (1) and (2), we can solve for J and E.

Subtracting equation (2) from equation (1):

(J - 5E) - (J - E) = 216 - 72
-J + 4E = 144

Simplifying the equation:

4E - J = 144 ----(3)

Now we have a system of equations (2) and (3) which can be solved simultaneously.

Solving the system of equations:

Adding equation (2) and equation (3):

J - E + 4E - J = 72 + 144
3E = 216
E = 72

Substituting the value of E into equation (2):

J - 72 = 72
J = 144

Therefore, Joyce has 144 seashells and Eunice has 72 seashells.