Question

The mass of 4.5 cm3 of iron and 8 cm3 of copper is equal to 101.5g. The mass of 3 cm3 of iron is 6.8g greater than the mass of 2 cm3 of copper. Find the density of iron and the density of copper

Answer 1

The answer
m is the density of iron, and M is the copper's. so m=M=101.5g
the mass of 3 cm3 of iron is 6.8g ≥ the mass of 2 cm3 of copper.
first, we know the formula
m= d x v, where m is the mass, d is the density and v is the volume;
the density of the iron is d= m /v (from the formula m= d x v). It is d= 6.8/3=2.26 g/cm3. It was assumed that m≥M=d x 2, so 6.8≥2xd, it implies
d is less than 3.4, (d≤6.8/2=3.4)
so the density of the copper is d ≤ 3.4

Answer 2

The density of iron is 7.8 g/cm³ and density of copper is 8.3g/cm³

Explanation:

The mass of 4.5 cm³ of iron and 8 cm³ of copper is equal to 101.5g.

The mass of 3 cm³of iron is 6.8g greater than the mass of 2 cm³ of copper.

Let the density of iron be x g/cm³ and density of copper be y g/cm³

Mass = Volume x Density

For sentence: "The mass of 4.5 cm³ of iron and 8 cm³ of copper is equal to 101.5"

`4.5x+8y=101.5----------(1)`

For sentence: "The mass of 3 cm³of iron is 6.8g greater than the mass of 2 cm³ of copper"

`3x=2y+6.8-------------(2)`

Now we will solve for x and y using elimination method.

`4.5x+8y=101.5]* 1`

`3x-2y=6.8]* 4`

`4.5x+8y=101.5`

`12x-8y=27.2`

Add both equation and eliminate y

`16.5x=128.7`

`x=7.8`

Put x=7.8 into equation 1

`4.5(7.8)+8y=101.5`

`8y=66.4`

`y=8.3`

Hence, The density of iron is 7.8 g/cm³ and density of copper is 8.3g/cm³