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How to solve the following math problem?
Old silver contains 90% silver. Silver solder contains 63% silver. If you wanted to make 200 kilograms of an alloy containing 82% silver, how many kilograms of old coins and how many kilograms of silver solder could you melt together to do this?
My teacher explained this in school today, and I was doing S.S. homework because I usually already know the things she teaches.
However, she told us to use a chart like the one below to do it
% Amount of Silver
Metal
___________________________
l l l l
Coin l l l l
l_______l___________l________l
l l l l
Solder l l l l
l_______l___________l________l
l l l l
Total l l l l
l_______l___________l________l
P.S. I think she called it combination, I am in 8th grade advances pre-algebra/Algebra 1
the chart got messed up, it should be 3x3, with Coin, Solder, and Total on the list going down; and percent, amount of metal, and silver going across the top.
2 Answers
- Anonymous1 decade agoFavorite Answer
The server removes spaces that it thinks are junk data. Instead use a place holder.
The table you want to use, with the information provided is:
******** % | Amount of Silver | Metal
___________________________
********l******** l********l ********l
Coin **l**90% l********l ********l
********l______l______l______l
*******l******** l********l ********l
Solder l**63% l********l ********l
********l______l______l______l
********l******** l********l ********l
Total **l**82% l********l 200kg*l
********l______l______l______l
Now, 82% of 200 kg is 164kg of silver, completing the last row. I'm also adding four variables to the table so that I can write a few equations.
******** % | Amount of Silver | Metal
___________________________
********l******** l********l ********l
Coin **l**90% l****A***l ***B***l
********l______l______l______l
*******l******** l********l ********l
Solder l**63% l****C***l ***D***l
********l______l______l______l
********l******** l********l ********l
Total **l**82% l*164kg*l 200kg*l
********l______l______l______|
From the table, you can see that B+D=200kg, A+C=164kg, A = 90% B, and C = 63% D.
From here, it's algebra to solve:
.9B+.63D=164kg
B=(164kg-.63D)/.9
(164kg-.63D)/.9+D=200kg
(1-.63/.9)D=200kg-164kg/.9
D=(200kg-164kg/.9)/(1-.63/.9)=1600/27=59.259259259259259259259259259...................................
Substitute D into the original equations to fill all four remaining slots in the table.
- ?Lv 44 years ago
look on the final 2 coefficients in the equation, ask your self, what numbers multiply to equivalent -5 and upload to equivalent 4? the respond is 5 and -one million: (5•-one million = -5 and 5 + -one million = 4) So now plug them into the x - r format: x^2 + 4x - 5 = (x - one million)(x + 5) = 0 now set each and all the standards equivalent to 0, remedy, after which you will have your 2 solutions x - one million = 0 x = one million x + 5 = 0 x = -5
