1) The weight of a glass bowl and the marbles it contains is 50 ounces. If the number of marbles in the bowl is doubled, the total weight of the bowl and marbles is 92 ounces. What is the weight of the bowl? (Assume that each of the marbles has the same weight).
2) Square ABCD and rectangle AEFG each have an area of 36 square meters. E is the midpoint of AB. What is the perimeter of rectangle AEFG? 3) A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 A.M. What time will the slow clock show when the correct clock shows 10 o'clock the evening of the same day? Solutions 1) Method 1: Since the weight of one bowl and the marbles it contains is 50 ounces, the weight of two bowls and twice as many marbles is 100 ounces. It is given that the weight of one bowl and twice as many marbles is 92 ounces. Then the difference of weights between 100 ounces and 92 ounces is the weight of the bowl, or 8 ounces. Method 2: The increase in weight from 50 ounces to 92 ounces occurs because the weight of the marbles is doubled. That increase therefore is the weight of the original set of marbles, 42 ounces. If follows that the bowl weighs 8 ounces. 2) The length of a side of the square is 6m. The dimensions of rectangle AEFG are 3m and 12m. The perimeter of the rectangle is 2 x (3m + 12m) which is equivalent to 30 m. 3) There are 13 hours between 9 AM and 10 PM. Thus the slow clock will lose 13 x 3 or 39 minutes and show 9:21 or 21:21 on a 24hour clock.
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