Question

The sum of three numbers is 10. The first number minus the second number plus the third is 6. The first minus the third is 2 more than the second. Find the numbers.

I've got so far,

x + y + z =10
x - y + 3 = 6

I can't figure out the third equation.

Answer 1

x-z=2+y

Answer 2

I think

Answer 3

correct

Answer 4

now solve the ssytem

Answer 5

x + y + z =10
x - y + 3 = 6
x-z=2+y
solve the third for x
x= 2+y+z
plug that into the second and solve for y
2+y+z - y + 3 = 6
z+5 = 6
z=1
x+y+z=10
x+y+1=10
2+y+1+y+1=10
2y+4 = 10
y=3
x = 6

Answer 6

Thanks so much for your help!

Answer 7

@zzr0ck3r
Hold on, I think you did the wrong equations!

The sum of three numbers is 10.
x+y+z = 10

The first number minus the second number plus the third is 6.
x-y+z = 6

The first minus the third is 2 more than the second. Find the numbers.
x-z=y+2

Answer 8

Different answer as a result...

Answer 9

This isn't right....because 6 + 3 + 1 equals 10 but 6 - 3 + 1 doesn't equal 6...

Answer 10

woops, sorry

Answer 11

yeah, you read "third" as 3 instead of "z"...

Answer 12

yeah, someone fix:) I got to go take a final :( sorry

Answer 13

This illustrates my argument that you *always* need to plug the answers back into all of the equations and make sure they actually are a valid solution :-)

Answer 14

So, thanks! Good luck with the final :-)

Answer 15

@zzelinski do you want to try solving the corrected system?

Answer 16

Yeah I was checking it and it didn't make sense...and yes I would!

Answer 17

(medal awarded for checking and spotting the error!)

Answer 18

@zzr0ck3r thanks for the help anyways and good luck on your final!

Answer 19

I think I checked the first one and thought it was good.
x+y+z=10
x-y+z=6
x-z=2+y
so x= 2+y+z
so
x-y+z=6 ----> 2+y+z-y+z=6
2z=4
z=2
x+y+z=10 ---> 2+y+2+y+2=10
2y=4
y=2
x = 2+2+2 = 6

Answer 20

x=6, y=2, z=2

Answer 21

I think that's right:)

Answer 22

I hope you see how I did it, if not ask any questions.

Answer 23

Yeah, with a system of equations, it's possible to have solutions to some equations turn out correct even though others do not. that's why you need to try them all. last set of answers agrees with mine, and check out: 6+2+2 = 10, 6-2+2=6, 6-2=2+2 :-)

Answer 24

Yes! Thank you all so much! I worked through the problem and got (6,2,2) as well.

Answer 25

Great! When checking my work, I like to reread the original statement, too — I discovered the first time I worked this problem that I'd thought the second sentence was "the first number minus 4 times the second number ..." and had I simply checked my solution in my equations, I wouldn't have noticed the error.

Answer 26

Or read the thing at all... I just went with what they said the equations was:)