Question 663902
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.