A farmer's heritage

A farmer died leaving his 17 horses to his 3 sons.
When his sons opened up the Will it read:
My eldest son should get 1/2 (half) of total horses;
My middle son should be given 1/3rd (one-third) of the total horses;
My youngest son should be given 1/9th (one-ninth) of the total horses.

How many horses should each son-heir get?

Correct result:

a =  9
b =  6
c =  2

Solution:

$$\begin{gathered} q={\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{3}}+{\displaystyle \frac{1}{9}}={\displaystyle \frac{17}{18}}\doteq 0.9444 \\ {q}_1=1-q=1-0.9444={\displaystyle \frac{1}{18}}\doteq 0.0556 \\ {n}_1=17 \\ {a}_1=n_1\mathrm{/}2=17\mathrm{/}2={\displaystyle \frac{17}{2}}=8.5 \\ {b}_1=n_1\mathrm{/}3=17\mathrm{/}3={\displaystyle \frac{17}{3}}\doteq 5.6667 \\ {c}_1=n_1\mathrm{/}9=17\mathrm{/}9={\displaystyle \frac{17}{9}}\doteq 1.8889 \\ {n}_2=1\mathrm{/}{q}_1=1\mathrm{/}0.0556=18 \\ a=n_2\mathrm{/}2=18\mathrm{/}2=9 \end{gathered}$$

$b=n_2\mathrm{/}3=18\mathrm{/}3=6$

$$\begin{gathered} c=n_2\mathrm{/}9=18\mathrm{/}9=2 \\ \text{ Verifying Solution: } \\ {n}_3=a+b+c=9+6+2=17 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• 9.A
  9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
• Salat
  Grandmother planted salad. In each row he planted 13 seedlings. After a morning frost many seedlings died. The first row five seedlings died. In the second row two seedlings died more than 1st row. In the third row three seedlings died less than 1st row.
• Diophantus
  We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth las
• Divide
  How many different ways can three people divide 7 pears and 5 apples?
• A laundry
  Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
• Drawing from a hat
  When drawing numbers from a hat from 1 to 35, we select random given numbers. What is the probability that the drawn numbers will be divisible by 8 and 2?
• Ducats
  The king divided the ducats to his three sons in a ratio of 2: 5: 4. How many ducats the king divided them if the youngest received 260 ducats, which was the least of all sons.
• Gold inheritance
  The king divided the inheritance with his three sons in the ratio of 7: 6: 4. Two of them received 286,000 gold. How much each of the sons got.
• Sales stores
  The first sales store passed the 1/3 and the second 2/5 of the total amount of goods.In third store passed the 2/3 rest of the goods. The remaining 40 kg of goods put into fourth store. How many kilograms of goods pass to a third store?
• Ravens
  The tale of the Seven Ravens were seven brothers, each of whom was born exactly 2.5 years after the previous one. When the eldest of the brothers was 2-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cu
• Father and son
  Father is three times older than his son. Twelve years ago, the father was nine times more senior than the son. How old are father and son?
• Final exam
  At the final exam, the student answers from three areas, which are evaluated in a ratio of 1: 2: 2. What grade will John receive if he answered as follows: 3,1,2.
• Father and sons
  Father is 27 and his sons 2 and one year. In how many years will his sons sum up to half his age?
• To improper fraction
  Change mixed number to improper fraction a) 1 2/15 b) -2 15/17
• Father and sons
  After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now?
• Alloy
  The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to
• Three monks
  Three medieval monks has task to copy 600 pages of the Bible. One rewrites in three days 1 page, second in 2 days 3 pages and a third in 4 days 2 sides. Calculate for how many days and what day the monks will have copied whole Bible when they begin Wednes