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.
d = desk
c = chair
Equation:
d + c = 200
d = 4c
Substitute 4c for d in first equation and solve for c. Insert that value into the second equation and solve for d. Check by inserting both values into the first equation.
To solve this problem using a system of equations, let's assign variables to the cost of the chair and the cost of the desk.
Let's say the chair costs C dollars, and the desk costs D dollars.
According to the given information, the desk costs four times more than the chair. This can be expressed as:
D = 4C
We also know that the combined cost of the desk and chair is $200:
C + D = 200
Now we have a system of two equations:
D = 4C
C + D = 200
To solve this system, we can use substitution or elimination method. Let's use substitution:
From the first equation, D = 4C
Substitute this value of D into the second equation:
C + 4C = 200
5C = 200
C = 200/5
C = 40
Now, substitute the value of C back into the first equation to find D:
D = 4(40)
D = 160
Therefore, the chair costs $40 and the desk costs $160 as a set.