Question

Marta looked at the results for the USA in the 2004 summer Olympics and noticed that the number of silver medals was 6 ​fewer (less)​ than twice the number of bronze medals. She also saw that the number of gold medals was ​four more than​ the number of silver medals. If the USA won 52 medals in total that year, how many of each type did they win?

Answer 1

Gold : 22 medals , Silver : 18 medals, Bronze : 12 medals

Explanation:

Solution:-

- Denote the total number of medals won by USA, T = 52

- The number of bronze medals = x

- The number of silver medals = y

- The number of gold medals = z

- We are given that number of silver medals (y) was 6 ​fewer (less)​ than twice the number of bronze medals (x). So the mathematical representation of this observation would be:

y = 2x - 6

- Similarly, the number of gold medals (z) was ​four more than​ the number of silver medals (y). So the mathematical representation of this observation would be:

z = y + 4

- The total number of medals T:

T = x + y + z

- We have 3 equations and 3 unknowns. Solve the equations simultaneously,

z = 2x - 6 + 4 = 2x - 2

T = x + ( 2x - 6 ) + ( 2x - 2)

52 = 5x - 8

5x = 60

x = 12 bronze medals

z = 2x - 2

z = 2*12 - 2

z = 22 gold medals

z = y + 4

y = 22 - 4

y = 18 silver medals

Answer 2

Answer: They won 22 gold, 18 silver and 12 bronze.

Step-by-step explanation: Suppose gold is g, silver is s and bronze is b.

The number of silver was 6 less than twice of bronze: s = 2b - 6

Gold was 4 more than silver: g = s + 4

Total is 52: g + s + b = 52

We have 3 equations and 3 variables. To determine each one:

s = 2b - 6 (1)

g = s + 4 (2)

g + s + b =52 (3)

Substitute (1) in (2):

g = 4 + 2b - 6

g = 2b - 2 (4)

Using (1) and (4), substitute in (3)

2b - 2 +2b - 6 + b = 52

5b = 52+8

b=
`(60)/(5)`

b = 12

With b, we find s:

s = 2.12 - 6

s = 18

With s, we find g:

g = 4 + 18

g = 22

Therefore, the team won 22 gold, 18 silver and 12 bronze.