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?

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=

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.

6e14 is the answer.