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The price of a conference table is \$419.99.
The budget is \$2000.
I need 6 chairs. The price of one of those chairs is \$199.99
If x is the price of a chair what algebraic equation can be written to represent this problem?

Reviewing the problem, since the variable X is the price per chair, the first solution is more appropriate.
Folks, the question posed is, "what algebraic equation can be written to represent this problem?"

They're looking for an equation, not a solution.

This question seems kind of silly given that they already told you what the price of a chair is, but if you pretend you don't know that information, you are left with this:

x = cost of 1 chair
Need: 6 chairs
Table costs: \$419.99
Budget: \$2000

The question could then be rephrased to read something like "How much could you afford to spend on 1 chair?"  The equation used to find the answer to that question (and to represent the problem that you described) is:

6x + 419.99 = 2000
There are two ways to attack this problem.  One is to try and find out the maximum price possible per chair and see if our price per chair is under that.  The other is to calculate the overall cost using our price per chair and see if that is under our budget.

Since you say x is the price of a chair, we are trying to see what is the maximum price you can pay per chair per your \$2000 budget.

B = Budget (maximum cost)
T = Table
X = Maximum price per chair

Therefore:
B = T + 6X
2000 = 419.99 + 6X
1580.01 = 6X
X = \$263.34 (rounded up to nearest penny)
Therefore, we can buy the chairs since they are less than \$263.34.

The second method would be:

C = 419.99 + 6(199.99)
C = 419.99 + 1199.94
C = 1619.93
Since the Cost is less than our \$2000 budget we can buy the chairs and table.

Let T = total cost of table plus chairs.

Then T = \$419.99 + (6)*(199.99) = \$1,619.93

Since \$1,619.93 < \$2,000.00 you do have enough money to complete the project.

\$2,000.00 - \$1,619.93 = \$380.07.

The fact that you came in "under budget" will make you a hero with your supervisor!
Hi Sara;
(budget)≥(6 chairs + 1 table)
(budget)≥(6x+t)
\$2000≥[(6)(\$199.99)]+(\$419.99)
\$2000≥\$1199.94+\$419.99
\$2000≥\$1619.93
I do not know if you are familiar with > and <.  When I was in the sixth grade, the way we remembered this is...
The alligator is going to eat the bigger one.
The alligator prefers the budget of \$2000.
Therefore, your purchases will survive and your conference room will be furnished.