One number is one more than two times another. If the sum is decreased by four the result is six. Find the numbers.

Answer 1

Let's call the two numbers X and Y, just so that they have a name. If one number is one more than two times the other number, we can write that as X + 1 = 2Y, and if the sum decreased by 4 is 6, that's saying that X+Y - 4 = 6.

So we have a system of equations: X+1 = 2Y and X+Y - 4 = 6. We can move things around a little bit and get:

X+1 = 2Y

X+Y=10

as our systems of linear equations.

Subtract the bottom one from the top one and you have 1-Y = 2Y-10. We do this to eliminate the X's and get Y by itself. Now we can conclude the 11 = 3Y, hence Y=11/3.

Then we can look at the original first equation, X+1 = 2Y, and since we know Y, we can get X.

X+1 = 2*(11/3), so X+1 = 22/3, X+ 3/3 = 22/3 (to get a common denominator), and X=19/3.

So our numbers are 11/3 and 19/3.