to qualify for a certain car loan, a customer must have a credit score of at least 600. in addition, the cost of the car must be at least $5000. define variables, write a system of ineaqualities to represent this situation, and name one possible solution.
Let's define the variables:
C = Credit Score of the customer
P = Cost of the car
The system of inequalities representing this situation is:
C ≥ 600 (Credit score should be at least 600)
P ≥ $5000 (Cost of the car should be at least $5000)
One possible solution could be:
C = 650 (Credit score of 650)
P = $8000 (Cost of the car is $8000)
This satisfies both inequalities as the credit score (C) is greater than or equal to 600, and the cost of the car (P) is greater than or equal to $5000.
To define the variables, let's use:
x: Credit score
y: Cost of the car
Now, to represent the given situation as a system of inequalities:
1. The customer must have a credit score of at least 600, so the first inequality is:
x ≥ 600
2. The cost of the car must be at least $5000, so the second inequality is:
y ≥ $5000
A possible solution to this system could be:
x = 650 (credit score)
y = $8000 (cost of the car)
In this example, the customer has a credit score of 650, which is greater than the minimum required score of 600. Additionally, the cost of the car is $8000, which is higher than the minimum required amount of $5000. Hence, the customer would qualify for the car loan with these values.
s = score
c = cost
s >= 600
c >= 5000
In the absence of any other qualifiers, any pair (s,c) such as (650,8623) satisfies the conditions.