Ratios of total number

Question

In the Summer Olympics in Sydney in 2000, the United States won gold silver, and bronze medals. The ratio of gold to silver medals was 5/3. The ratio of silver medals to bronze medals was 8/11. What were the total numbers of gold, silver, and bronze medals won by the United States?

Answer 1

g/s = 5/3, s/b =8/11

3g=5s, 11s =8b

s= 8b/11

3g =5(8b)/11 = 40b/11

33g = 40b

3 equations with no unique solution,

an infinite number of solutions

3g =5s

11s =8b

33g = 40b

gold = 40n

silver =24n

bronze =33n

where n=any integer

most simple solution is g=40, s=24, b=33

but it could also be g=80, s=48, b=66

or g=120, s=72, b= 99

practical limitations tend to eliminate higher multiples

actual US medals in 2000 summer Olympics were

37 gold, 24 silver, 32 bronze

40,24 and 33 is close