The sum of three numbers is 1000. The sum of the first and second numbers is 650, the sum of the second and third is 550. Find out each of the numbers.
Let us denote the required numbers by x1, x2 and x3.
According to the condition of the problem, the sum of these three numbers is 1000, therefore, the following relationship takes place:
x1 + x2 + x3 = 1000.
It is also known that the sum of the first and second numbers is equal to 650, and the sum of the second and third numbers is equal to 550, therefore, the following relations take place:
x1 + x2 = 650;
x2 + x3 = 550.
We solve the resulting system of equations.
Subtracting the second from the first equation, we get:
x1 + x2 + x3 – x1 – x2 = 1000 – 650;
x3 = 350.
Subtracting the third from the first equation, we get:
x1 + x2 + x3 – x2 – x3 = 1000 – 550;
x1 = 450.
Substituting the obtained values for x3 and x1 into the equation x1 + x2 + x3 = 1000, we get:
450 + x2 + 350 = 1000;
800 + x2 = 1000;
x2 = 1000 – 800;
x2 = 200.
Answer: the required numbers are 450, 200 and 350.
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