Gabriela coleciona moedas e em sua coleção há 165 moedas de ouro,220 moedas de prata e 275 moedas de bronze. Ela deseja organizar essa coleção em caixas que tenham o mesmo número de moedas e de tal modo que cada caixa contenha o maior número possível de moedas de um só tipo.Nessas condições,quantas moedas Gabriela deve colocou-se em casa causa

55 coins in each box (12 boxes in total)

Step-by-step explanation:

The question in english is as follows:

Gabriela collects coins and in her collection there are 165 gold coins, 220 silver coins and 275 bronze coins. She wants to organize this collection in boxes that have the same number of coins and in such a way that each box contains the largest possible number of coins of a single type.

Under these conditions, how many coins Gabriela should put in each box?

So, we have 165 gold coins, 220 silver coins and 275 bronze coins, which sum in total 660 coins.

If we want to organize these coins in boxes with the same number of coins, we have to calculate the greatest common divisor among these three numbers:

Divisors for 165: 33, 5, 1

Divisors for 220: 44, 5, 1

Divisors for 275: 55, 5, 1

As we can see, the greatest common divisor is 55, this means we have to put 55 coins of the same type in each box.

In addition, taking into account we have a total of 660 coins; if we divide this by 55 we have as a result 12 boxes.

Therefore, Gabriela has to put 55 coins of the same type in 12 boxes.

Given:

The system of equations is:

To find:

The solution for the given system of equations.

Solution:

We have,

           ..(i)

         ...(ii)

Multiply equation (i) by 4, to make common coefficient of x.

           ..(iii)

Subtract (ii) from (iii).

Putting in (i), we get

Therefore, the solution of the given system of equations is .