A desk and a chair cost $200 as a set. If the desk costs four times more than the chair, how much does each one cost. Write and solve using a system of equations.
c + 4c = 200
5c = 200
c = 40
The chair costs $40.
To solve this problem using a system of equations, let's assign variables to the unknown quantities.
Let's call the cost of the chair "c" and the cost of the desk "d".
According to the problem, we know that the desk costs four times more than the chair, so we can write the first equation as:
d = 4c
We also know that the total cost of the desk and chair set is $200. This can be written as:
d + c = 200
Now we have a system of equations:
1) d = 4c
2) d + c = 200
We can solve this system by substitution or elimination. Let's use substitution to solve it.
We'll substitute the value of d from equation 1 into equation 2:
4c + c = 200
5c = 200
c = 200/5
c = 40
Now, substitute the value of c back into equation 1 to find d:
d = 4(40)
d = 160
Therefore, the chair costs $40 and the desk costs $160.