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wo friends Bill and Tony want to evaluate each sum shown below and round it to the nearest whole number. Bill decides to take a shortcut by first rounding off each number in the sum to the nearest whole number, and then adding the whole numbers. Tony decides to round each sum the correct way, by first adding the decimals and then rounding the sum off to the nearest whole number. For how many of the following sums do Bill and Tony reach the same final answer? $\bullet$ (a) $33.3 + 33.33 + 33.333$ $\bullet$ (b) $7.9 + 3.8 + 9.1$ $\bullet$ (c) $19.5 + 12.7 + 13.1$ $\bullet$ (d) $17.6 + 17.7 + 13.15$ As an example, if Bill and Tony are given the sum $0.1 + 0.1 + 0.1,$ Bill will perform these steps:$$0.1 + 0.1 + 0.1 \, \rightarrow \,0 + 0 + 0 \,\rightarrow \,0,$$while Tony will perform these steps:$$0.1 + 0.1 + 0.1 \, \rightarrow \, 0.3 \, \rightarrow \, 0.$$

 Jun 21, 2020
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Billy and Tony reach the same final answer for (a) and (c).

 Jun 21, 2020

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