1/5 of J's money is equal to 1/3 of S's money. The difference in their amount is 1/2 of A's money. If Adam gives $120 to S, S will have the same amount of money as J. How much do the 3 people have altogether?(please show me a model method, not algebra)

1/5 J= 1/3 S

J-S=1/2 A

S+120=J

Well, looking at the last equations, it is obvious that J-S=120

then A=240

J-S=120
3J-5S=0 From first equation.

3J-3S=360
3J-5S=0
2S=360
S=180
finally, J=300

Sum them up.

To solve this problem using a model method, we can use a diagram to represent the information given and the relationships between the people.

Let's represent the amount of money J has as J's money (J), the amount of money S has as S's money (S), and the amount of money A has as A's money (A).

1/5 of J's money is equal to 1/3 of S's money:
We can represent this relationship by dividing J's money into 5 equal parts and S's money into 3 equal parts. We know that 1 part of J's money is equal to 1 part of S's money.

The difference in their amount is 1/2 of A's money:
We can represent this relationship by taking the difference between the amounts of J and S and making it equal to half of A's money.

Now let's follow the given information step by step:

1. Divide J's money into 5 equal parts.
2. Divide S's money into 3 equal parts.
3. One part of J's money is equal to one part of S's money.
4. Take the difference between the amounts of J and S and make it equal to half of A's money.
5. Adam gives $120 to S, so we subtract $120 from S's amount.

To find the total amount of money they have altogether, we add the amounts of J, S, and A.

Now, we can assign any value to one of the variables, let's say we assign J = $300.

Based on the information above, we can use the diagram to find the values of S and A.

- Since 1/5 of J's money is equal to 1/3 of S's money, we have:

J's money (J) = $300
S's money (S) = (1/5) * J = (1/5) * $300 = $60

- The difference in their amount is 1/2 of A's money:

Difference in amounts = J - S = $300 - $60 = $240
(1/2) * A = $240

Therefore, A = (2 * $240) = $480

- Adam gives $120 to S, so S's new amount is $60 + $120 = $180.

To find the total amount of money they have altogether, we add J, S, and A:

Total amount = J + S + A
= $300 + $180 + $480
= $960

Therefore, the three people have $960 altogether.