SOLUTION: at the present time a man is four times as old as his son six years ago he was 10 times as old.

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Question 708800: at the present time a man is four times as old as his son six years ago he was 10 times as old.
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = th eage of the dad
Let B = the age of the son
Equation 1: A+=+4B
Equation 2: A+-+6+=+10%2A%28B-6%29
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Since equation 1 is solved for A, plug 4B into equation 2 for A
Equation 2: A+-+6+=+10%2A%28B-6%29
%284B%29+-+6+=+10%2A%28B-6%29
Multiply the 10 through
4B+-+6+=+10B+-+60
Subtract 4B from both sides
-6+=+6B+-+60
Add 60 to both sides
54+=+6B
Divide both sides by 6
highlight%289+=+B%29
Now plug 9 into equation 1 for B
Equation 1: A+=+4B
A+=+4%2A%289%29
highlight_green%28A+=+36%29
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Extra question #1:
The line y=mx+c passes through (2'5) and (4'13). Find the m and the c.
In that equation m is the slope and c is the Y-intercept.
Points on a graph are given in the form (X,Y).
The equation to find the slope of the line between to points is:
m+=+%28Y2-Y1%29%2F%28X2-X1%29
Now we will plug in the values you were given to solve for m.
m+=+%2813-5%29%2F%284-2%29
m+=+8%2F2
highlight_green%28m+=+4%29
Since we know what m equals, we can rewrite the equation of the line.
y = mx+c is now y = 4x+c
The next step is to pick one of the points that you were gven and solve for c.
I will you the point (2,5)
That means that when x=2, then y=5
Plug those values into the line equation
y+=+4x+%2B+c
5+=+4%2A2+%2B+c
5+=+8+%2B+c
Subtract 8 from both sides
highlight%28-3+=+c%29
The equation of the line that passes through the given points is y = 4x - 3
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Extra question #2:
Twice one Number added to 3 times a nother gives 21. Find the numbers if the difference between them is 3.
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Equation 1: 2A+%2B+3B+=+21
Equation 2: A+=+B+%2B+3
Since equation 2 is solved for A, plug (B + 3) into equation 1 for A.
Equation 1: 2A+%2B+3B+=+21
2%2A%28B+%2B+3%29+%2B+3B+=+21
Multiply the 2 through
2B+%2B+6+%2B+3B+=+21
Combine like terms
5B+%2B+6+=+21
Subtract 6 from both sides
5B+=+15
Divide both sides by 5
highlight%28B+=+3%29
Now plug 3 into equation 2 for B.
Equation 2: A+=+B+%2B+3
A+=+%283%29+%2B+3
highlight_green%28A+=+6%29