Edema of the pkg
1) After mom took half, remained1/2, after borrowing the older brother, 1/4 remained, after the father 1/8, after the sister 1/8 - 3/5 = 3/40. If 30 cm is 3/40 of the initial length, the desired length is 30: 3/40 = 400 centimeters, or 4 meters.
2) Let the clock break through the x. The cash amount of points should be denoted by 2x. If there were twice as many of them, that is, 4x, then this number would exceed three times the number of clock strokes at the next combat, i.e. (x + 1). As follows, we have the equation 4x / 3 = x + 1, whence x = 3. It was 3 hours.
3) We denote the number of available chairs by x. Then the number of students can be expressed dual: by 3 (x + 5) and by 4 (x - 3). Both expressions must be equal, whence we have equation
Solving it, we find x = 27. As it should, the chairs were 27, and the pupils 3 - (27 + 5) = 96.
4) We denote the distance between the houses by x. The young man just passed 2, and the doctor is four times less, that is, x / 2-. Before the meeting, the doctor went through half of the way he had traveled, i.e., x / 4, and the young man - the rest, i.e. 3x / 4. The doctor passed his part of the way at x / 12 hours, and the young man - at 3x / 16 hours, while we know that he was on the road for 3/4 hours longer than the doctor. We have the equation:
whence = 2.4 kilometers. So, from the house of a young man to the doctor's house - 2,4 kilometers.
5) Filling 300 grams of water in a cup of weights,weigh this "water weight" at first 300 grams of tea. Then, putting these 300 grams of tea on one cup, we put on the other buckle, that is, 650 grams, and pour so much tea on the least loaded bowl into a separate bag so that the balance is in balance, ie 350 grams Having weighed 650 grams of tea with a buckle, we have 650 g + 350 g = 1000 g, i.e. 1 kilogram.
6) Denote the prime cost of the 1st watermelon through x. Then the net profit from the realization of the first watermelon of the first batch is 36th, 2nd 32nd, third 27th, after all, the last watermelon of the 48th. Because the net profit from the sale of each batch is similar, the number of watermelons in the first batch should be equated
All these expressions, according to the condition of the problem, the entity is an integer. It is necessary, as it should, to choose for - a value at which expressions
are converted to integers. It is easy to find, by the method of several tests, that this condition is satisfied only by - = 24. Then the 1st expression is 2, the 2nd is 3, the third is 8. In other words, in the first batch there were 2 watermelons, in the 2nd 3, in the third 8. In total, watermelons were brought by a merchant 2 + 3 + 8 + 1 = 14.
7) The method of the second student is more convenient, becausemultiplication of 1 year 1 month. 1 1/4 days on 4 - we immediately get rid of the fraction, then multiplication by 9 is made easier. The method of the first student does not provide such amenities, it is more massive. Therefore, the teacher had to give the second solution a higher score.
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