June Wedding Math - The Solutions
06/21/2004

We can see that the formula Rate × Time = Distance will be useful with this problem. We know that the entire trip is 2 × 290 = 580 miles and that the entire time to complete the round-trip was 5.5 + 7.75 = 13.25 hours. Now we have R × 13.25 = 580. Dividing both sides by 13.25 yields R = 43.8 miles per hour, to the nearest tenth.

We’ve been given a lot of information! The song itself is 5 × 60 + 30 = 330 seconds long. Additionally, we have five bridesmaids, each taking a 43-second walk, which will account for 5 × 43 = 215 seconds. Taking this time, as well as the 10 seconds of the song that play before the first bridesmaid starts, we have 330 – 215 – 10 = 105 seconds left over. This time will be spread evenly over the four pauses that will occur between consecutive bridesmaids, so there will be 105 ÷ 4 = 26 seconds, to the nearest whole number, between the end of one and the beginning of the next.

We know that we have 137 guests. Since this is an odd number, and only one of our table sizes is an odd number, then we have at least one 11-person table and 126 guests left over. Since we want the most 12-person tables we can get, we can perform 126 ÷ 12 = 10.5 to see that there can’t be more than 10. Ten of these tables would seat 120 people with 6 left over, and this isn’t an option. Nine of these tables would seat 9 × 12 = 108 people with 18 left over, which again can’t be split between 11- and 10-person tables. Eight 12-person tables will seat 96 people with 30 people left over. These 30 people can be accommodated by three 10-person tables, so our answer is 8.

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