The sum of three numbers is 301. The second number is 3 less than twelve times the first number. The third number is 4 more than seven times the number. Find the three numbers.
first number is 910/39,the second one is 3601/13and the third one is 2/3
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The sum of three numbers is 301. The second number is 3 less than twelve times the first number. The third number is 4 more than seven times the what number. Find the three numbers.
To find the three numbers, let's assign variables to represent each number and translate the given information into equations.
Let's say the first number is "x", the second number is "y", and the third number is "z".
From the given information, we have three equations:
1) The sum of three numbers is 301: x + y + z = 301
2) The second number is 3 less than twelve times the first number: y = 12x - 3
3) The third number is 4 more than seven times the first number: z = 7x + 4
Now, we can solve this system of equations to find the values of x, y, and z.
First, let's express one equation in terms of a variable and substitute it into the other equations.
From equation 2, we have y = 12x - 3. We can substitute this expression for y in equations 1 and 3.
Substituting y in equation 1: x + (12x - 3) + z = 301
Simplifying equation 1: 13x + z = 304 ------(4)
Substituting y in equation 3: z = 7x + 4
Now, let's solve this system of equations.
Using substitution, we can substitute equation 4 into equation 3.
13x + z = 304 -----(4)
-7x + z = 4 -----(5)
Subtracting equation 5 from equation 4, we get:
(13x - 7x) + (z - z) = 304 - 4
Simplifying:
6x = 300
x = 50
Now that we have the value of x, we can substitute it back into equation 2 to find the value of y.
y = 12x - 3
y = 12(50) - 3
y = 597
Finally, we can substitute the values of x and y into equation 3 to find the value of z.
z = 7x + 4
z = 7(50) + 4
z = 354
Therefore, the three numbers are:
x = 50
y = 597
z = 354