Find two numbers...

[idosew]

My 6th grader has this problem to solve...I'm not sure what suggestions to give her.
Two numbers have the same seven digits in the same order. The greatest digit is in the millions place. The least digit is in the ten-thousandths place. The difference between the numbers is 1,975,427.4375. What are the two numbers?
Answers would be helpful, but more importantly, what tools do you use to solve this?
Thanks in advance.

 

[Loren]

My 6th grader has this problem to solve...I'm not sure what suggestions to give her.
Two numbers have the same seven digits in the same order. The greatest digit is in the millions place. The least digit is in the ten-thousandths place. The difference between the numbers is 1,975,427.4375. What are the two numbers?
Answers would be helpful, but more importantly, what tools do you use to solve this?
Thanks in advance.

This doesn't make sense to me. If you have a seven digit number whose largest digit is in the millions place and you are to subtract a seven digit number whose smallest digit is in the ten-thousandths place, you would have to add some zeros to the first number to accomplish the subtraction. If you add zeros to the first number, it is no longer a seven digit number. Zero is a digit. I rather suspect that either this is not the exact wording of the problem, or it is a trick problem of some sort.
A,BCD,EFG.0000
0,000,HJK.LMNP
1,975,427.4375

It is obvious that P must be a 5, having had to borrow one from the zero in the thousandths place, making it a 9. Then, N must be a 2, since 9-2=7. You might proceed this way and carry on, but this assumes that zero is not a digit. Also, if P = 5, then there must be some duplication of the digits in the subtrahend, because they all must be greater or at least equal to 5. Furthermore, 2 is less than 5, and that violates the condition that the smallest digit is P.

I'm voting in favor of it's being a trick problem.

 

[idosew]

Okay, after doing a 'plug & chug' I came up with a solution. It isn't as much a trick as an exercise...

First, don't assume anything about the leading digits of the 2nd number or the digits to the right of the decimal in the first. I started with a 9 all the way to the right and worked my way left...

1,975,624.9999
- 0,000,197.5624 Once I got those four 9's in place, that dictated the next left-most digits.
_______________
1,975,427.4375

 

[Denis]

Okay, after doing a 'plug & chug' I came up with a solution. It isn't as much a trick as an exercise...

First, don't assume anything about the leading digits of the 2nd number or the digits to the right of the decimal in the first. I started with a 9 all the way to the right and worked my way left...

1,975,624.9999
- 0,000,197.5624 Once I got those four 9's in place, that dictated the next left-most digits.
_______________
1,975,427.4375

Problem clearly states: "The greatest digit is in the millions place"
That's 9,???,???.

 

[Loren]

But the "greatest digit" could be a 2, if all the other digits are 1's and 0's.

 

[Denis]

But the "greatest digit" could be a 2, if all the other digits are 1's and 0's.

Ya; so: 2,???,???
All I was trying to do is show WHERE "the millions place" is.