Question 391694: I need help on the following word problem: A ring is made out of gold and copper. Gold has a density of 19.3 g/cm3. Copper has a density of 9 g/cm3. Mass m, density d, and volume v are related by the formula m=dv. The ring has a volume of 8.4 cm3, and a mass of 104.44g.
Let a=volume of gold, let c=volume of copper, mass of gold =dv=19.3a, mass of copper=dv=9c.
Solve the following system by elimination to find out how many grams of gold are in the ring.
a+c = 8.4
19.3a+9c=104.44
also what is the percent of gold by mass?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! I need help on the following word problem: A ring is made out of gold and copper. Gold has a density of 19.3 g/cm3. Copper has a density of 9 g/cm3. Mass m, density d, and volume v are related by the formula m=dv. The ring has a volume of 8.4 cm3, and a mass of 104.44g.
Let a=volume of gold, let c=volume of copper, mass of gold =dv=19.3a, mass of copper=dv=9c.
Solve the following system by elimination to find out how many grams of gold are in the ring.
a+c = 8.4..............................1
19.3a+9c=104.44........................2
multiply (1)by -9
-9a-9c=-75.6
add this to (2)
19.3a-9a+9c-9c=104.44-75.6
10.3a=28.84
/10.3a
a=28.84/10.3
a= 2.8 cm^3 = volume of gold
a+c=8.4
plug value of a
2.8+c=8.4
c=8.4-2.8
c=5.6 cm^3 volume of copper
...
mass of copper = 5.6*9= 50.4 gm
....
d gold = 19.3 gm/cm^3
m=19.3*2.8
mass of gold = 54.04 gm.
...
Total mass of ring = 54.04+50.40=104.44 gm
...
gold % = (54.04/104.44)*100
gold % = 51.74
...
m.ananth@hotmail.ca
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