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?
A(x) = 700 + 20x
B(x) = 1200 + 15x
set A(x) = B(x) to find for what x they are the same
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.
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.