Elements of Algebra

CHAP. III. OF ALGEBRA. 195 these two parts, taken together, ought to make $a$; so that $2x - b = a$; adding $b$, we have $2x = a + b$, wherefore $x = \frac{a+b}{2}$, which is the value of the greater part; and that of the less will be $\frac{a+b}{2} - b$, or $\frac{a+b}{2} - \frac{2b}{2}$, or $\frac{a-b}{2}$. 586. Question 3. A father leaves 1600 pounds to be divided among his three sons in the following manner; viz. the eldest is to have 200 pounds more than the second, and the second 100 pounds more than the youngest. Required the share of each. Let the share of the third son be $x$ Then the second's will be - - - $x + 100$; and The first son's share - - - - $x + 300$. Now, these three sums together make 1600*l*.; we have, therefore, $3x + 400 = 1600$ $3x = 1200$ and $x = 400$ The share of the youngest is 400*l*. That of the second is - - 500*l*. That of the eldest is - - 700*l*. 587. Question 4. A father leaves to his four sons 8600*l*. and, according to the will, the share of the eldest is to be double that of the second, minus 100*l*.; the second is to receive three times as much as the third, minus 200*l*.; and the third is to receive four times as much as the fourth, minus 300*l*. What are the respective portions of these four sons? Call the youngest son's share $x$ Then the third son's is - $4x - 300$ The second son's is - - $12x - 1100$ And the eldest's - - - $24x - 2300$ Now, the sum of these four shares must make 8600*l*. We have, therefore, $41x - 3700 = 8600$, or $41x = 12300$, and $x = 300$. Therefore the youngest's share is 300*l*. The third son's - - - - - 900*l*. The second's - - - - - 2500*l*. The eldest's - - - - - 4900*l*. 588. Question 5. A man leaves 11000 crowns to be divided between his widow, two sons, and three daughters. He intends that the mother should receive twice the share of a son, and that each son should receive twice as much O 2