Luiza João tem juntos R$123 se Luiz tivesse a mais metade da quantia que tem mais um real teria dobro de João quanto tem cada um

A=25

B=98

Step-by-step explanation:

You can see it as a 2-eq system.

Call A Joao's money and B Luiz's money. The sum is $123:

A + B = 123

As the half of Luiz's money + 1 is the double of Joao's money, we could represent this as:

(B/2) + 1 = 2A [this is what the last sentence says]

We can get the A value by dividing both sides by 2:

[ (B/2) + 1]/2 = 2A / 2

B/4 + 1/2 = A

Then, replacing this A value on our first equation:

B/4 + 1/2 + B = 123

B/4 + 4B/4 = 123 - 1/2

(5/4) B = 122.5

Multiplying by (4/5) [or dividing by 5/4] to eliminate this 5/4:

(5/4) B * (4/5) = 122.5 (4/5)

B = 98

Then we find A:

A = B/4 + 1/2 = 24.5 + 0.5 = 25

A=25