Can you help me with my math?
Topic: Can you help me with my math?
June 16, 2019 / By Charissa Question:
Old silver coins contain 90% silver. Silver solder contains 63% silver. If you wanted to make 200 kilograms of an alloy containing 81% silver, how many kilograms of old coins and how many kilograms of silver solder could you melt together to do this?
Best Answers: Can you help me with my math?
Antonette | 9 days ago
Ahhh, ye olde % problem that most teachers are unable to clearly explain.
Call x the kg's of old coins you need and y the kg's of silver solder.
Then the total kg's must add up to 200, so the first equation is x+y = 200
Next, there are x*0.90 kg of silver in the old coins and y*0.63 kg of silver in the silver solder.
So, the total amount of silver is 0.90x +0.63y. This must be 81% of the total mass, i.e. 0.81*200.
So, your second equation is 0.9x+0.63y = 162
You solve for x and y. Simple enough?
👍 266 | 👎 9
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Let silver = x and silver solder =y
since x+y must =200, therefore x =200 -y
.90(x) +.63y =.81(200)
.90(200 -y) +.63y =.81(200)
lets rid fraction by multiplying all by 100
90(200-y) +63y = 81(200)
18000-90y +63y = 16200
1800 = 27y
66.67 =y =kg of silver solder coins
200 -66.67 = x =133.33 = kg of 90% silver coins
👍 110 | 👎 2
x := the weight of silver coins
y := the weight of silver solder
x+y = 200
90x+63y = 200*81
multiply the first equation by 63 and subtract it from the second
27x = 200*(81-63) = 3600
x = 133.3 kg
y = 66.7 kg
👍 102 | 👎 -5
Let x kg of coins be mixed with y kg of solder.
In x kg coins, solver=9x/10 kg.
In y kg solder, silver=63/100 kg.
133.33 kg of coins are to be mixed with 66.66 kg of solder.
Hope this helps!!!
👍 94 | 👎 -12