In Ali garden, he wants to build a concrete fountain. So he consults two different companies who provides concrete pours: Alibaba's Concrete (charges $700 plus $20/m^3 of concrete) and Baborina's Concrete ($1200 plus $15/m^3 of concrete). Let x be the totalm^3 of concrete pours need.

Question

In Ali garden, he wants to build a concrete fountain. So he consults two different companies who provides concrete pours: Alibaba's Concrete (charges $700 plus $20/m^3 of concrete) and Baborina's Concrete ($1200 plus $15/m^3 of concrete). Let x be the totalm^3 of concrete pours need.

Find an algebraic expression for both companies in terms of x and for what volume of concrete will it be cheaper to use Alibaba's Concrete?

Answer 1

A(x) = 700 + 20x

B(x) = 1200 + 15x

set A(x) = B(x) to find for what x they are the same

Answer 2

Let's define the cost function for both companies in terms of x:

Alibaba's Concrete cost function: C(x) = 700 + 20x, where x is the total volume of concrete pours needed.

Baborina's Concrete cost function: C(x) = 1200 + 15x, where x is the total volume of concrete pours needed.

Now, let's find the volume of concrete for which it will be cheaper to use Alibaba's Concrete.

We need to find the value of x for which the cost of Alibaba's Concrete is lower than Baborina's Concrete.

So, we set up the inequality:

700 + 20x < 1200 + 15x

Now, let's solve this inequality to find the range of values for x where Alibaba's Concrete is cheaper.

700 + 20x - 15x < 1200

5x < 500

Divide both sides by 5:

x < 100

Therefore, when the volume of concrete needed is less than 100m^3, it will be cheaper to use Alibaba's Concrete.

The algebraic expression for Alibaba's Concrete cost: C(x) = 700 + 20x

The algebraic expression for Baborina's Concrete cost: C(x) = 1200 + 15x

Note: If the volume of concrete needed is exactly 100m^3, both companies will have the same cost.

Answer 3

To find an algebraic expression for both companies in terms of x, we can use the given information:

For Alibaba's Concrete:
Cost = $700 + $20/m^3 * x

For Baborina's Concrete:
Cost = $1200 + $15/m^3 * x

Now, we need to determine at what volume of concrete it will be cheaper to use Alibaba's Concrete.

To do this, we need to set the two expressions equal to each other and solve for x:

$700 + $20/m^3 * x = $1200 + $15/m^3 * x

Now, we can solve for x:

$20/m^3 * x - $15/m^3 * x = $1200 - $700

($20 - $15)/m^3 * x = $500

$5/m^3 * x = $500

To find the volume of concrete (x) at which Alibaba's Concrete is cheaper, we can solve for x:

x = $500 / ($5/m^3)

Simplifying this:

x = $500 * (m^3/$5)

x = 100 * m^3

Therefore, it will be cheaper to use Alibaba's Concrete for a volume of concrete pours less than 100 cubic meters.