A school wants to purchase some round tables and some rectangular tables. The costs of one round table and one rectangular table are $20 and $25, respectively. The school wants to spend at most $1,000. Represent this
problem for the purchase of x round tables and y rectangular tables graphically
20x+25y <= 1000
for a graphical solution, see
http://www.wolframalpha.com/input/?i=plot+20x%2B25y+%3C%3D+1000
To represent the problem graphically, we need to create a coordinate plane with x and y axes. In this case, the x-axis will represent the number of round tables (x), and the y-axis will represent the number of rectangular tables (y).
The equation for the cost of the round tables is given as $20 per table, so the equation can be represented as:
Cost of round tables = 20x
Similarly, the equation for the cost of the rectangular tables is given as $25 per table, so the equation can be represented as:
Cost of rectangular tables = 25y
The school wants to spend at most $1,000. Therefore, the total cost of the tables should not exceed $1,000. This can be represented as:
Total cost of tables = 20x + 25y ≤ 1000
Now, we can plot the equation 20x + 25y = 1000 on the coordinate plane:
- First, convert the equation to slope-intercept form (y = mx + b):
25y = -20x + 1000
y = (-20/25)x + 1000/25
y = (-4/5)x + 40
- Choose different values for x and calculate corresponding y values:
For x=0, y = 40
For x=5, y = 36
For x=10, y = 32
For x=15, y = 28
For x=20, y = 24
- Plot the points (0,40), (5,36), (10,32), (15,28), and (20,24) on the graph, and draw a line connecting them.
This graph will represent the feasible combinations of round tables and rectangular tables that the school can purchase without exceeding their budget.