Depth · one concept from first principles · step 2 of 4
Evan walked 0.2 km less than 0.7 times Nami's 1.9 km. First multiply 0.7 by 1.9, then subtract 0.2.
Breaking a hard sentence into 'multiply, then subtract' is exactly the order words like 'less than 0.7 times' tell us to use.
5.NBT.B.7Identify SubproblemsEvan's distance is seven tenths of Nami's, with 0.2 km taken off that amount.
Taking 0.7 of Nami's 1.9 km means cutting that distance into ten equal parts and keeping seven of them.
The 0.2 km is said to be how much less Evan walked than that amount, so it comes off the seven-tenths share and not off Nami's distance.
Jacob walked 1.8 times Evan's 1.13 km, so multiply 1.8 by 1.13.
Now that Evan's distance is a known number, Jacob's becomes a plain decimal multiplication.
5.NBT.B.7Identify SubproblemsLine up the three distances in kilometers and compare: Nami 1.9, Evan 1.13, Jacob 2.034. The largest is Jacob's.
Since every distance is in the same unit (km), I can compare the numbers directly to see who went farthest.
5.NBT.B.7Analyze The UnitsWhen each answer depends on the one before it, solve the steps in order, one at a time.
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The same shape shows up later on the AMC, as Branching State Enumeration, Lattice / Grid Pattern from Small Cases, Small-Domain Constrained Search. Why the shapes repeat →