SOLUTION: I am having a hard time figuring out this word problem: The sum of three numbers is 98. The sum of the first and second is two more than the third number, and the second is for mo

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Question 72541: I am having a hard time figuring out this word problem:
The sum of three numbers is 98. The sum of the first and second is two more than the third number, and the second is for more than the first. Find the numbers.
So far I have figured out the equations but can't seem to put them together to solve the equation:
x+y+z=98
x+y=2+z
y=4+x
Found 3 solutions by Earlsdon, josmiceli, stanbon:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, your first steps are good. Now you have three equations in three unknowns, x, y, and z.
1) x+y+z = 98
2) x+y = 2+z
3) y = 4+x
Substitute equation 3) into equation 2) and solve for z.
2a) x+(4+x) = 2+z Simplify and solve this for z.
2a) 2x+4 = 2+z
2a) z = 2x+2
Now substitute equation 3) (y = 4+x) and equation 2a) (z = 2x+2) into equation 1) and solve for x.
1a) x+(4+x)+2x+2) = 98 Simplify and solve for x.
1a) 4x+6 = 98
1a) 4x = 92
1a) x = 23 This is the first number.
3) y = 4+x
3) y = 4+23
3) y = 27 This is the second number.
2a) z = 2x+2
2a) z = 2(23)+2
2a) z = 46+2
2a) z = 48 This is the third number.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+y+%2B+z+=+98
x+%2B+y+-+z+=+2+
add these
2x+%2B+2y+=+100
x+%2B+y+=+50
also
y+=+x+%2B+4
x+-+y+=+-4
x+%2B+y+=+50
add these
2x+=+46
x+=+23 answer
y+=+x+%2B+4
y+=+23+%2B+4
y+=+27 answer
x+%2B+y+%2B+z+=+98
23+%2B+27+%2B+z+=+98
50+%2B+z+=+98
z+=+48 answer
check
23+%2B+27+%2B+48+=+98
98+=+98
OK
x+%2B+y+-+z+=+2+
23+%2B+27+-+48+=+2
2+=+2
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x+y+z=98
x+y=2+z
y=4+x
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Try substitution from the bottom of the list.
I end up with x+4++x+2x+2=98
4x+6=98
4x=92
x=23
y=27
z=48
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Cheers,
Stan H.