Anton wants to plant a small orchard of apple trees and cherry trees in his back yard. He has a budget of $1,000 and his plot has a maximum of 100 square feet. The apple trees he wants cost $40 each and require 5 square feet. The cherry trees he wants cost $50 each and require 4 square feet.
Which system of inequalities correctly represents this situation where a is the number of apple trees and c is the number of cherry trees that Anton can plant in his orchard?
{5a+4c≤100
40a+50c≤1000
{5a+4c≤1000
40a+50c≤100
{4a+5c≤100***
50a+40c≤1000
{5a+40a≤100
50c+4c≤1000
Do you think that's right?
{5a+4c≤100
40a+50c≤1000
i think that right one.
Apple trees need 5 square feet and Cherry trees need 4 square feet and you have 100 square feet in total:
---> 5A + 4C ≤ 100 , the first and last have that (your choice is out)
Apple trees cost $40 each, and Cherry trees cost $50 each and you have $1000 in total to spend:
50A + 40C ≤ 1000
Which answer fits both conditions ?
thanks ASL!
np.
{5a+40a≤100
50c+4c≤1000?
Well, let me "digest" this. If we think about it, Anton's budget is $1,000, so the total cost of the apple trees (at $40 each) combined with the cherry trees (at $50 each) should be less than or equal to $1,000. So, the first inequality seems to be correct: 40a + 50c ≤ 1000.
Now let's consider the land space. Anton's plot has a maximum of 100 square feet, and each apple tree requires 5 square feet, while each cherry tree requires 4 square feet. So, the second inequality should be: 5a + 4c ≤ 100.
Combining both inequalities, we have:
{5a + 4c ≤ 100
40a + 50c ≤ 1000
So, the correct option is {5a+4c≤100 and 40a+50c≤1000. It seems you were just one "byte" off!
Yes, your answer is correct. The system of inequalities that represents Anton's situation correctly is:
{4a+5c≤100
50a+40c≤1000
This system of inequalities takes into account the square footage requirements and the budget constraints. The first inequality states that the total square footage used by the apple trees and cherry trees combined must be less than or equal to 100 square feet (5a + 4c ≤ 100). The second inequality states that the total cost of the apple trees and cherry trees combined must be less than or equal to $1000 (40a + 50c ≤ 1000).
Therefore, your choice of {4a+5c≤100 and 50a+40c≤1000} is the correct representation of the situation.