Respuesta :
Answer:
Country A won 78 medals
Country B won 26 medals
Country C won 15 medals
Step-by-step explanation:
We have been given with :-
A+B+C=119 _____equation(1)
B=C+11 ____equation(2)
A=B+C+37 ____equation(3)
1) Starting with the 3rd equation,
A=B+C+37
2) Subtract 37 from both sides
A-37=B+C+37-37
3) Cancelling out +37 and -37 from the right side we get,
A-37 = B+C
or
B+C = A-37
4) Plugin B+C= A-37 in the equation 1,
A+B+C = 119
=> A+(A-37) = 119
=> 2A-37 = 119
5) Add 37 to both sides
2A-37+37=119+37
6) Cancelling out -37 and +37 from the left side, we get
2A = 156
7) Divide both sides by 2
[tex]\frac{2A}{2} =\frac{156}{2}[/tex]
8) Cancelling out the 2's on the left side, we get
A = 78
9) Now, we plugin A=78 in the equation 1
A+B+C=119
=> 78+B+C=119
10) Subtract 78 from both sides
78+B+C-78 = 119 -78
11) Cancelling out +78 and -78 from the left side, we get
B+C= 41 ____let it be equation (4)
12) Subtracting C from both the sides of the equation 2, we get
B=C+11
=> B-C = C+11 - C
13) Cancelling out +C and -C from the right side, we get
B-C= 11 _____let it be equation (5)
14) Adding the equations 4 and 5, we get
B+C+B-C=41+11
15) Cancelling out the +C and -C, we get
2B = 52
16) Divide both sides by 2
[tex]\frac{2B}{2}=\frac{52}{2}[/tex]
17) Cancelling out the 2's on the left, we get
B = 26
18) Substituting A= 78 and B= 26 in the equation (1), we get
A+B+C=119
=> 78+26+C=119
=> 104+C=119
19) Subtracting 104 from both the sides, we get
104 + C - 104 = 119 -104
20) Cancelling out +104 and -104 from the left side, we get
C = 15
