Question

In an athletics​ event, a team earned 2 more gold medals than silver. The number of silver medals that the team earned was the same as the number of its bronze medals. The team earned a total of 17 medals. How many of each kind of medal did the team​ earn? A. Gold B. Silver C. Bronze

Answer 1

The team earned 7 gold medals, 5 silver medals, and 5 bronze medals.

Step-by-step explanation:

To solve the problem of determining how many of each kind of medal an athletics team earned, let's denote the number of silver and bronze medals as ‘S’, and thus the number of gold medals will be ‘S + 2’. Since it is given that the team earned the same number of silver and bronze medals, and the total number of medals is 17, we can set up the following equation:

G + S + B = 17

Substituting the number of gold medals ‘G’ with ‘S + 2’ because the team earned 2 more gold than silver, and knowing that the number of silver medals is equal to the number of bronze medals (‘S = B’), we get:

(S + 2) + S + S = 17

Simplifying the equation:

3S + 2 = 17

We then subtract 2 from both sides to isolate the terms with ‘S’:

3S = 15

And divide by 3 to find the value of ‘S’, which represents the number of silver and bronze medals:

S = 5

Since ‘S’ is 5, the number of gold medals is ‘S + 2’, which equals 7.

Therefore, the team earned 7 gold medals, 5 silver medals, and 5 bronze medals.