Question

The length of a pool has to be three times the size of the width plus 3, and the depth has to be 7 less than twice the length.
Create expressions to represent the dimensions of the pool.
Determine the polynomial expression to represent the area of land space that the pool will cover.
Using the area and the depth expressions, determine the polynomial expression that is used to represent the volume.
Classify the volume polynomial by degree and number of terms.

Answer 1

To fit the dimensions of the various land spaces, he realizes that the length of the pool has to be three times the size of the width plus 3 and the depth has to be 7 less than twice the length.
Task 1

Create expressions to represent the dimensions of the pool.

Create a variable to represent the width of the pool. Determine the expressions to represent length and the depth in terms of the width variable.
Determine the polynomial expression to represent the area of land space that the pool will cover.
Using the area and the depth expressions, determine the polynomial expression that is used to represent the volume.
Classify the volume polynomial by degree and number of terms.

I'd suggest you pick several literals (variables) to represent the pool dimensions. Why not L, W and D for length, width and depth respectively?

If the length of the pool is to be three times the width, plus 3 feet, how would you represent that in terms of W? L = ??

Once you have an expression for the length, L, how would you write an expression for D, the depth, first, in terms of L, and then in terms of W?

Answer 2

Thanks. I was able to get that far... it's the second part. Where it says determine the polynomial expression etc. Everything from that point on I don't know how to do.

Answer 3

They just want L x W for the polynomial dealing with land space. What i would do, Is relate L and W to D. Solve for W and L with those relations involving D, then calculate the product LD.

Answer 4

Can you give me an example? I'm not askin for the answer I'm just still a bit confused.

Answer 5

Sure. Like this question, let l =2w + 4 and d = 3l - 5. We can substitute for l and we have d = 3(2w + 4) - 5. From here, we can solve for w, and since we already l = (d + 5)/3, we can calculate lw. In this example lw = ((d + 5)/3) * ((d-7)/6)

Answer 6

** we already have l = (d+5) / 3 **

Answer 7

Ohhhhh!!! Okay! Thanks.