Respuesta :
Answer:
Country A won 79 medals, country B won 29 medals and country C won 16 medals.
Step-by-step explanation:
This question is solved by a system of equations.
I am going to say that:
Country A won x medals.
Country B won y medals.
Country C won z medals.
Total of 124 medals:
This means that [tex]x + y + z = 124[/tex].
Country B won 13 more medals than Country C.
This means that [tex]y = z + 13[/tex]
Country A won 34 more medals than the total amount won by the other two.
This means that:
[tex]x - (y + z) = 34[/tex]
From the first equation, we have that:
[tex]y + z = 124 - x[/tex]
So
[tex]x - (y + z) = 34[/tex]
[tex]x - (124 - x) = 34[/tex]
[tex]2x - 124 = 34[/tex]
[tex]2x = 158[/tex]
[tex]x = \frac{158}{2}[/tex]
[tex]x = 79[/tex]
Finding z:
Since [tex]x = 79, y = z + 13[/tex]
[tex]x + y + z = 124[/tex]
[tex]79 + z + 13 + z = 124[/tex]
[tex]2z + 92 = 124[/tex]
[tex]2z = 32[/tex]
[tex]z = \frac{32}{2} = 16[/tex]
Finding y:
[tex]y = z + 13 = 16 + 13 = 29[/tex]
Country A won 79 medals, country B won 29 medals and country C won 16 medals.
