1) A bicyclist wants to make a 600mile trip on his twowheel bicycle. He has a spare wheel which is used to replace either of the other two wheels. Suppose each of the three wheels is to have the same mileage for the trip. How many miles should each wheel travel?
2) How many even numbers between 1 and 101 are multiples of 3? 3) In the subtraction problem below, all five of the digits 3, 5, 6, 7, and 9 are to be placed, one in each box. What is the smallest difference that can be the result? Solutions 1) No matter which two wheels are actually used at any time during the 600mile trip, the total miles traveled by those wheels together is 1200 miles. Since three wheels are to share that total equally, each will travel 400 miles. 2) The even multiples of 3 are 6, 12, 18, . . . The largest multiple of 6 less than 101 is 16 x 6 = 96. Multiples of 6 less than 101 are: 1 x 6, 2 x 6, 3 x 6, 4 x 6, . . . , 16 x 6. There are 16 even multiples of 3 between 1 and 101. 3) Make the 3digit number as small as possible and the 2digit number as large as possible, as shown at the right. The smallest possible difference is 259. 3 5 6  9 7 2 5 9
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