is a, that of the new one is the altitude, h, of a regular triangle with the side a, or
a/ 3
In neither case are any of the plants closer to
each other than the minimum distance. To find the ratio of the number of plants in each case we have to figure the ratio of the width of both strips, in other words, to divide a by a
* The 2 result is 2 V 3 or approximately 1.15. Thus, by dividing the field into regular triangles instead of squares the farmer is in a position to plant about 15 percent more -and to harvest accordingly. 113 - The unit price of the farmer's geese was i dollar, that of his neighbor's geese, i dollar, hence the average price of each goose of the combined flock should have been dollar. 65 When selling five geese for two ( (3 + 2 ) . 60 = 6-0 dollars, the farmer in effect sold at a unit price of 2 or dollar. Therefore, his unit price was 1 dollar too low and the result, considering that 60 geese were sold, was a deficit of 60 X i = I dollar. 114 - If the younger of the brothers, B, can split only i of what the older boy, A, can saw, then A's performance is 4 that of B's. When the younger boy saws and the older one uses the axe, we have the relation I: 2, so we have this tabulation: While A splits x,
B saws 2 2
While B splits y,
A saws 4y s3
Now x + y = 5 and- 2+ -y = 5. Hence x = 2 andy =8. 2 3 B saws I cord A splits 2, That means that A saws 4 cords and B splits 3, and thus both split 5 and saw 5 cords. 115 -If we call the original number of chickens x, and of the ducks, y, and the increase factor of the chicken and ducks 3a and a, respectively, we have the equation x + 3ax + y + ay = 200. We also have the equation x + y = 25 for the original flock. Knowing that all unknowns, x, y and a, must be whole numbers, we can determine their values. The farmer's wife started her business with 5 chickens and 20 ducks. She had a 15 fold increase in chickens and a 5 fold increase in ducks. Today she owns 80 chickens and 120 ducks. 136