Word problem

Question

To qualify for a certain needs a scholarship a student must get a score of at least 75 on a qualification test in addition the students family must make less than $40,000 a year define the variables write a system of inequalities to represent the situation and then one possible solution

Answer 1

S = score

F = family income

 

S ≥ 75          At least 75

F < 40000     less than 40000

 

A student would receive a scholarship with a score of 80 and family income of $30,000.

Answer 2

We will call the variable that describes the test score as S, which is a pretty obvious choice. The other variable is buried in the text of the problem. What happens if the family makes more that $40,000? The problem says that the family will not be eligible for the scholarship. Let's call that income variable I.

 

S = score on the test

I = family income

 

The MINIMUM value for the score is 75. In math-speak, that means that S has to be greater or equal to 75. "At least" means the given value plus anything greater.

 

S ≥ 75

 

For the income, the family needs to make LESS than $40,000. Note that the problem says less than, but does not say "or equal to". Therefore we do not include the equal bar in the inequality.

 

I < $40,000

 

To find a possible value, choose an S and an I value from the inequalities we just found.

 

I hope this helps!