2. While on Amazon, you decide to keep shopping. You have wanted to buy a desk and chair so that you have a place to do your homework. The chair is $35 less than the desk. The two items together will cost $175 (tax is included). Use an algebraic equation to calculate the cost of each piece of furniture.
Let's assume the cost of the desk is x dollars.
According to the information given, the chair is $35 less than the desk, so the cost of the chair would be (x - $35) dollars.
Now, the total cost of both items together, including tax, is $175.
So, the equation to represent this situation is:
x + (x - $35) = $175
To solve this equation, we simplify it:
2x - $35 = $175
Next, we isolate the variable:
2x = $175 + $35
2x = $210
Finally, we solve for x by dividing both sides of the equation by 2:
x = $210/2
x = $105
Therefore, the desk costs $105 and the chair costs ($105 - $35) = $70.
Let's assign variables to the cost of the desk and the chair. Let's say the cost of the desk is D and the cost of the chair is C.
We know that the chair is $35 less than the desk, so we can write this as an equation:
C = D - 35 (equation 1)
We also know that the two items together will cost $175. So, the sum of the desk and chair's cost is equal to $175:
D + C = 175 (equation 2)
We can use these two equations to solve for the cost of each piece of furniture. Since equation 1 is already solved for C, we can substitute it into equation 2:
D + (D - 35) = 175
Now, we can solve for D:
2D - 35 = 175
Add 35 to both sides:
2D = 210
Divide both sides by 2:
D = 105
Now that we know the cost of the desk (D = $105), we can substitute it back into equation 1 to find the cost of the chair:
C = 105 - 35
C = 70
Therefore, the desk costs $105 and the chair costs $70.