Question 663902: At the 2006 Winter Olympics in Italy, the top medal winner was Germany, which won a total of 29 medals. Germany won 1 more silver medal than gold and 5 more gold medals than bronze. Find the number of each type of medal won. How do I solve this?
Found 3 solutions by ewatrrr, ReadingBoosters, Theo:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
1 more silver medal than gold and 5 more gold medals than bronze
bronze
Gold: (x+5)
Silver: (x+5) + 1 Or (x+6)
Question states***total of 29 medals
x + (x+5) + (x+6) = 29 ||Solve for x and then determine the # of gold and Silver as well
Answer by ReadingBoosters(3246)  (Show Source):
You can put this solution on YOUR website! x = bronze
y = silver
z = gold
x+y+z=29
y=z+1
z=x+5
Substitute into the x+y+z equation
(z-5) + (z+1) + z = 29
3z -4 = 29
3z = 29 +4
3z = 33
z = 11 gold medals
y = 11+1=12 silver medals
x = 11-5 = 6 bronze medals
...
Check
11+12+6=29
.......................
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! germany won 29 medals.
germany won 1 more silver medal than gold and 5 more gold than bronze.
let g = number of gold medals.
let s = number of silver medals.
let b = number of bronze medals.
the total number of medals won is 29 so you get:
g + s + b = 29
number of gold medals plus number of silver medals plus number of bronze medals = 29.
now look at the relationships between the quantities of each type of medal.
germany won 1 more silver than gold.
this means that s = g + 1 which translates to the number of silver medals is equal to the number of gold medals plus 1.
germany won 5 more gold medals than bronze.
this means that g = b + 5 which translates to the number of gold medals is equal to the number of bronze medals plus 5.
you have 3 equation so far.
they are:
g + s + b = 29
s = g + 1
g = b + 5
since s = g + 1, you can substitute for s in the original equation.
since g = b + 5, you can substitute for g in the original equation.
substitute for s first and then substitute for g.
when you substitute for s, g + s + b = 29 becomes g + (g + 1) + b = 29
simplify to get 2g + b + 1 = 29
now substitute for g to get:
2g + b + 1 = 29 becomes 2 * (b + 5) + b + 1 = 29
simplify to get 3b + 11 = 29
subtract 11 from both sides of the equation to get 3b = 18
divide both sides of the equation by 3 to get b = 6
from the equation g = b + 5, substitute for b to get g = 6 + 5 which becomes g = 11 after combining like terms.
in the equation s = g + 1, substitute for g to get s = 11 + 1 which becomes s = 12 after combining like terms.
you get:
b = 6
g = 11
s = 12
plug these values into the equation of g + s + b = 29 to see if the equation holds true.
you get 11 + 12 + 6 = 29 which becomes 29 = 29 which is true so you did good.
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