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

.......................

Delighted to help.

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Wanting for others what we want for ourselves.

www.MyHomeworkAnswers.com 

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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