andrewn4215
contestada

One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he conuted 74 heads and 196 legs. How many humans and horses were there

Respuesta :

dexteright02
Data:

Humans (x) = 2 Legs
Horses (y) = 4 Legs

74 Heads
196 Legs

Solving:

Addition method

[tex] \left \{ {{x + y =74} \atop {2x + 4y =196}} \right. [/tex]

Simplify by (-4) The first equation

[tex]\left \{ {{x + y =74(-4)} \atop {2x + 4y =196}} \right. [/tex]
[tex]\left \{ {{-4x - \diagup\!\!\!\!\!4y =-296} \atop {2x + \diagup\!\!\!\!\!4y =196}} \right.[/tex]
[tex]\left \{ {{-4x =-296} \atop {2y =196}} \right.[/tex]
[tex]-2x = -100.simplify(-1)[/tex]
[tex]2x = 100[/tex]
[tex]x = \frac{100}{2} [/tex]
[tex]\boxed{x = 50}[/tex]

Now, to find the number of horses, I will use the following equation and I will replace the found value, we will have:

[tex]x + y = 74[/tex]
[tex]50+y = 74[/tex]

Number with incognito are to the left of the equality and numbers without incognito are to the right, remembering that when changing of side changes the signal.

[tex]y = 74-50[/tex]
[tex]\boxed{y = 24}[/tex]

Answer:
Humans = 50
Horses = 24


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