SOLUTION: A bag contains 42 coins, with a total weight of 246 grams. If the bag contains only gold coins that weigh 8 grams each and silver coins that weigh 5 grams each, how many gold and

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A bag contains 42 coins, with a total weight of 246 grams. If the bag contains only gold coins that weigh 8 grams each and silver coins that weigh 5 grams each, how many gold and       Log On


   

Question 760541: A bag contains 42 coins, with a total weight of 246 grams. If the bag contains only gold coins that weigh 8 grams each and silver coins that weigh 5 grams each, how many gold and how many silver coins are in the bag?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = number of gold coins
Let b = number os silver coins
Equation 1: A+%2B+B+=+42
Equation 2: 8A+%2B+5B+=+246
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Solve equation 1 for one of the variables.
Equation 1: A+%2B+B+=+42
A+=+42+-+B
Now plug (42 - B) into equation 2 for A
Equation 2: 8A+%2B+5B+=+246
8%2A%2842+-+B%29+%2B+5B+=+246
Simplify the equation.
336+-+8B+%2B+5B+=+246
Combine like terms.
336+-+3B+=+246
Add 3B to both sides
336+=+246+%2B+3B
Subtract 246 from both sides.
90+=+3B
Divide both sides by 3.
highlight%2830+=+B%29
Now solve for A while using B = 30,
A+=+42+-+B
A+=+42+-+%2830%29
highlight_green%28A+=+12%29