In a recent international sport competition, the top three countrieslong dash—country a, country b, and country clong dash—won a total of 119119 medals. country b won 1111 more medals than country c. country a won 3737 more medals than the total amount won by the other two. how many medals did each of the top three countries win?

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

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

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

x is variable or an unknown value to find

example:

2x = 5 which means x = 3

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.