Question

In a recent international sport​ competition, the top three countries—Country ​A, Country​ B, and Country C—won a total of 124 medals. Country B won 13 more medals than Country C. Country A won 34 more medals than the total amount won by the other two. How many medals did each of the top three countries​ win?

Answer 1

Country A won 79 medals, country B won 29 medals and country C won 16 medals.

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
`x + y + z = 124`.

Country B won 13 more medals than Country C.

This means that
`y = z + 13`

Country A won 34 more medals than the total amount won by the other two.

This means that:

`x - (y + z) = 34`

From the first equation, we have that:

`y + z = 124 - x`

So

`x - (y + z) = 34`

`x - (124 - x) = 34`

`2x - 124 = 34`

`2x = 158`

`x = (158)/(2)`

`x = 79`

Finding z:

Since
`x = 79, y = z + 13`

`x + y + z = 124`

`79 + z + 13 + z = 124`

`2z + 92 = 124`

`2z = 32`

`z = (32)/(2) = 16`

Finding y:

`y = z + 13 = 16 + 13 = 29`

Country A won 79 medals, country B won 29 medals and country C won 16 medals.