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there was a seller of horses, who sold all his horses to three people. To the first man he sold half of all his horses and a half of a horse. to the second man he sold half of what he had left and half of a horse. To the third man he again sold half of what was left and a half of a horse. How many horses did he have at first?

Respuesta :

kikivanderwal

Answer:

17

Step-by-step explanation:

ajeigbeibraheem

The total number of horses he had at first was 7 horses.

What are word problems?

Word problems in mathematics involve careful understanding and they are those methods we use in solving real-life cases by using:

  • Basic arithmetic operations,
  • Fractions, and/or
  • Algebraic expressions etc.

From the given information:

  • Let the half of all his horses to the first man be x and half of a horse be y
  • Let half of what is left to the second man be z and half of a horse be y
  • Let half of what is left to the third man be a and half of a horse be y.

Then, we can have the system of equations for the three cases to be:

[tex]\mathbf{\dfrac{1}{2}x + \dfrac{1}{2}y = 3 ---- (1)}[/tex]

Making (y) the subject and ignoring (x), we have:

[tex]\mathbf{y = \dfrac{3 - \dfrac{1}{2}}{\dfrac{1}{2}} = 5}[/tex]

y = 5

For the second man;

[tex]\mathbf{\dfrac{1}{2}z + \dfrac{1}{2}y = 3 ---- (2)}[/tex]

[tex]\mathbf{z= \dfrac{3 - \dfrac{1}{2}(5)}{\dfrac{1}{2}} = 1}[/tex]

z = 1

For the third man:

[tex]\mathbf{\dfrac{1}{2}a + \dfrac{1}{2}y = 3 ---- (2)}[/tex]

[tex]\mathbf{a= \dfrac{3 - \dfrac{1}{2}(5)}{\dfrac{1}{2}} = 1}[/tex]

a = 1

Thus, the total number of horses he had at first were:

= 5 + 1 + 1

= 7 horses

Learn more about word problems here:

https://brainly.com/question/13818690

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