Problem
Rounding to the nearest hundred watches the tens digit, so the largest amount still rounding down is 35049.
Third graders learn the round-up/round-down line; testing 35049 versus 35050 shows exactly where the boundary sits.
3.NBT.A.1Guess And CheckRounding to the nearest thousand watches the hundreds digit, so the smallest amount still rounding up is 27500.
Checking the two numbers straddling the halfway mark pins down the lowest amount that still rounds to 28000.
3.NBT.A.1Guess And CheckThe gap is widest with one amount at its maximum and the other at its minimum, so pair 35049 with 27500.
Writing each person's possibilities as a range makes it obvious which endpoints give the widest gap.
6.EE.B.8Identify SubproblemsThe difference is greatest when Minchae's amount is taken at its largest and Junho's at its smallest.
A difference grows when the larger amount grows and grows again when the smaller amount shrinks, so both ends should be pushed as far apart as they will go.
Each saver's real amount may sit anywhere inside its own rounding band, and the two bands have nothing to do with each other, so the extremes can be chosen independently.
Rounding looks at the place just below the one being kept, and that place bundles ten of the next smaller unit, which is what fixes how wide the band is.
Subtract the smallest possible Junho amount from the largest possible Minchae amount.
A single multi-digit subtraction finishes the problem once the extreme amounts are known.
4.NBT.B.4Look For A PatternTo make a difference as big as possible, pick the largest the first number can be and the smallest the second number can be.