## If XX+YY=ZYZ, what are the values for X, Y and Z?

Fractions, ratios, percentages, exponents, number patterns, word problems without variables, etc.
zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

### If XX+YY=ZYZ, what are the values for X, Y and Z?

If XX+YY=ZYZ, what are the values for X, Y and Z?

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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Since the result for X + Y in the ones column is not the same as the X + Y for the tens column, there must be a "carry", so X + Y = 10 or more. But X + Y cannot equal 10 itself, since then Z = 0, and you can't have a leading zero. You know that X + Y must be 17 or less, since X and Y are different numbers, and 8 + 9 = 17.

Since you're adding two 2-digit numbers and getting a 3-digit number, there must be an additional "carry" when you add the X + Y + 1 in the tens column. The minimum value of X + Y is 11, and the maximum is 17, so the minimum and maximum for X + Y + 1 are 12 and 18. What is Z, in either case?

Then what must be X + Y? ...and so forth.

zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

### Re: If XX+YY=ZYZ, what are the values for X, Y and Z?

is X=5,Y=6 or X=6,Y=5?

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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Um... neither.

Check those values in the addition. Will they give you a correct value in the middle of ZYZ?

zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

### Re: If XX+YY=ZYZ, what are the values for X, Y and Z?

z=1
11=2+9=3+8=4+7=5+6
2+9 works
99+22=121
is that rite?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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If it works, it's right!

zackattack
Posts: 15
Joined: Wed Apr 01, 2009 12:51 pm

oky thnx