Considering the definition of an equation and the way to solve it, it will take 4 hours for both companies to equal the same price and it will cost $90 at that time.
Definition of equation
An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
- When a value that is adding, when passing to the other member of the equation, it will subtract.
- If a value you are subtracting goes to the other side of the equation by adding.
- When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.
- If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.
This case
First, you define the variable "t" as the time for the landscaping company to work on the backyard renovation. You know that:
- Company A charges a $50 fee to come out to your house plus $10 an hour to work.
- Company B charges $15 per hour and $30 to show up.
So the price of each company is:
- Price of company A=50 + 10t
- Price of company B=30 + 15t
If both companies equal the same price, the equation in this case is:
Price of company A= Price of company B
50+ 10t= 30 + 15t
Solving
50 - 30= 15t - 10t
20= 5t
20÷5= t
4=t
At this time, the price of both companies is
- Price of company A= 50+ 10t= 50 + 10×4= 90
- Price of company B= 30 + 15t= 30 + 15×4= 90
In summary, it will take 4 hours for both companies to equal the same price and it will cost $90 at that time.
Learn more about equations:
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