The sum of three numbers is 2008. The second is 2 less than twice the first and the third is 9 more than thrice the second.Find the three numbers?

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David Shabazi answered

The sum of three numbers is 2008. The second is 2 less than twice the first and the third is 9 more than thrice the second."The sum of three numbers is 2008."

Three numbers represent three different variables: X, y, and z. X is the first variable, y is the second, and z is the third. So it says the sum, meaning adding these three variables together, will give 2008.
x + y + z = 2008
"The second is 2 less than twice the first."
"2 less" means to add 2 to the variable that it's talking about, which is y in this case. And "twice the first" just means 2 times the first variable, which is x.
y + 2 = 2x
y = 2x - 2 (I simplified the equation to get a value for y so that it will be easier to find the values of all three numbers.)
"The third is 9 more than thrice the second."
"9 more" means to subtract 9 from the variable that it's talking about, which is the third variable (z) in this case. And "thrice the second" just means 3 times the second variable, which is y.
z - 9 = 3y

z = 3y + 9 (I also simplified this equation so that I could find the value of z more easily.)

We technically have values for y and z, in which we can plug them into the original equation we had, which was x + y + z = 2008. Plugging them in, we will get:

x + (2x - 2) + (3y + 9) = 2008

But hang on, there's still a y variable in the equation, and we have a value for y, so we can plug in more values.

x + (2x - 2) + [3(2x - 2) + 9] = 2008

Now we must simplify the equation and solve for x.

x + 2x - 2 + (6x - 6 + 9) = 2008

3x - 2 + 6x + 3 = 2008

9x + 1 = 2008

9x = 2007

x = 223

Now that we have a value for x, we can plug this into the other two equations for y and z

y = 2x - 2

y = 2(223) - 2

y = 446 - 2

y = 444

z = 3y + 9

z = 3(444) + 9

z = 1332 + 9

z = 1341

The three numbers are: x = 223, y = 444, and z = 1341.

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