Brian is creating a collage on a piece of cardboard that has an area of 120r3 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of the square root of r to the fifth power square centimeters. Use the given information to determine an expression for the total number of pieces of paper used.

Someone please help me :)

Question

Brian is creating a collage on a piece of cardboard that has an area of 120r3 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of the square root of r to the fifth power square centimeters. Use the given information to determine an expression for the total number of pieces of paper used. 

Someone please help me :)

jim_thompson5910 · Answer

So the overall area is $\Large 120r^3$ ?

and each piece has an area of $\Large \sqrt{r^5}$ ?

anonymous · Answer

Yess

jim_thompson5910 · Answer

let x = number of pieces needed

jim_thompson5910 · Answer

if you have x pieces, each of area with $\Large \sqrt{r^5}$ square units

then you'll have 

$\Large x*\sqrt{r^5}$

as the total area

jim_thompson5910 · Answer

So therefore, 

$$\Large x*\sqrt{r^5} = 120r^3$$ 

solve for x to get ???

anonymous · Answer

Okay so I'm confused on how to solve for x

jim_thompson5910 · Answer

you divide both sides by sqrt(r^5), then rationalize the denominator like this

$$\Large x*\sqrt{r^5} = 120r^3$$ 

$$\Large x = \frac{120r^3}{\sqrt{r^5}}$$ 

$$\Large x = \frac{120r^3*\sqrt{r^5}}{\sqrt{r^5}*\sqrt{r^5}}$$ 

$$\Large x = \frac{120r^3*\sqrt{r^5}}{\sqrt{(r^5)^2}}$$ 

$$\Large x = \frac{120r^3*\sqrt{r^5}}{r^5}$$ 

$$\Large x = \frac{120r^3*\sqrt{r^{4+1}}}{r^5}$$ 

$$\Large x = \frac{120r^3*\sqrt{r^{4}*r^{1}}}{r^5}$$ 

$$\Large x = \frac{120r^3*\sqrt{r^{4}}*\sqrt{r}}{r^5}$$ 

$$\Large x = \frac{120r^3*r^{2}*\sqrt{r}}{r^5}$$ 

$$\Large x = \frac{120r^{3+2}*\sqrt{r}}{r^5}$$ 

$$\Large x = \frac{120r^{5}*\sqrt{r}}{r^5}$$ 

$$\Large x = 120\sqrt{r}$$

anonymous · Answer

Okay...so would the answer be that equation or what? I'm awful at this stuff

jim_thompson5910 · Answer

well they want an expression, ie this $\Large 120\sqrt{r}$ 

because that represents the exact number of pieces needed

jim_thompson5910 · Answer

because we said "let x = number of pieces needed"

anonymous · Answer

So is the answer 120 sqrt. r?

jim_thompson5910 · Answer

correct

jim_thompson5910 · Answer

and those steps show why/how

anonymous · Answer

Okay so if i write all of that above and then make my final answer 120 sqrt. r thats it?

jim_thompson5910 · Answer

yes pretty much

anonymous · Answer

Thank you so much!

jim_thompson5910 · Answer

you're welcome