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Question 839507: 7. The sum of three whole numbers is 7. The second number is 1 more than the twice of the third number. The sum of first and third number is 3 less than the second number. Find all the three numbers.
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve this word problem, we need to set this up as equations. We are first told the sum of three whole numbers is 7. We can express this as:
x + y + z = 7, where x, y, and z represent our unknown numbers
Next, we are told the second number is 1 more than twice the third number. In other words
y = 2z + 1
Finally, we are told the sum of the first and third number is 3 less than the second number. In other words
x + z = y - 3
Now we have 3 equations, and we can solve by substitution.
Since our second equation is already solved for y, we can substitute that equation for y in one of our other two equations. Let's substitute the second equation for y in our third equation:
x + z = 2(1 + 2z) - 3 ----->
x + z = 2 + 4z - 3 ----->
x + z = 4z - 1
Now, let's solve for x, by subtracting z from both sides, giving us:
x = 3z - 1
Now, we can replace both x and y with 3z - 1 and 1 + 2z, respectively, into our first equation, x + y + z = 7:
(3z - 1) + (1 + 2z) + z = 7 ----->
3z - 1 + 1 + 2z + z = 7 ----->
6z = 7
Divide both sides by 6, to give us z:
z = 7/6
Next, we can replace z in our second equation (y = 1 + 2z), with 7/6 to obtain y:
y = 1 + 2(7/6) ----->
y = 1 + 14/6 ----->
y = 20/6
Since we now have z and y, we can substitute 7/6 and 20/6 for z and y in our first equation:
x + (20/6) + (7/6) = 7 ----->
x + 27/6 = 7
Finally, subtract 27/6 from both sides to obtain the value of z:
x = 7 - (27/6) ----->
x = 15/6
We now have our three numbers: 15/6, 20/6 which we can reduce to 10/3, and 7/6
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