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Question 631391: The metal used to make a coin is a mixture of steel and copper. The ratio, mass of steel : mass of copper is 108 : 7 The coin has a total mass of 230 milligrams Calculate the mass of copper in this coin.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let s represent the mass of steel in the coin
let c represent the mass of copper in the coin
the mass in the coin is equal to 230
your equation is:
s + c = 230
since the ratio of steel to copper is 108/7, this means that:
steel = 108/115 times the mass of the coin.
copper = 7/115 times the mass of the coin.
this results in steel = 216 milligrams and copper = 14 milligrams
the ratio of steel to copper is 216/14 = 108/7
the sum of the mass of steel and copper is 216 + 14 = 230
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another way to look at it:
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the ratio of steel to copper is 108/7
this means that 108*x + 7*x = mass of the coin.
this means that 108*x + 7*x = 230
combine like terms to get:
115*x = 230
solve for x to get 2
this means that 108*2 + 7*2 = 230 which results in:
216 + 14 = 230
this means the mass of the coin in steel is 216 milligrams and the mass of the coin in copper is 14 milligrams.
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still another way to look at it:
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ratio of steel to copper is 108/7
let s represent mass of steel
let c represent mass of copper
you get:
s/c = 108/7
solve for s to get s = 108c/7
you also know that s+c = 230
substitute for s in this equation o get:
108c/7 + c = 230
multiply both sides this equation by 7 to get:
108c + 7c = 230*7
combine like terms to get:
115c = 230*7
divide both sides of this equation by 115 to get:
c = 230*7/115 which results in c = 14
since s+c = 230, this means that s must be equal to 216.
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