Question

1) Derek purchased a new gym membership. It costs him seven dollars a month plus two dollars for every time that he visits the gym. He wants to spend less than 25 dollars a month to visit the gym. Write an inequality that models the situation using the variable V for the number of visits per month. Also find the maximum number of visits he can make to the gym and still keep his cost below 25 dollars a month.

2) In Gym class, Sue is shooting basketball free throws. She is shooting three sets of twenty shots each. In her first two attempts, she made 13 and 18 free throws. What are the possible scores on her third attempt if she is to have an average between 12 and 16 free throws after all three attempts? Express your answer in the form of a compound inequality using the variable F to represent a successful basketball free throw.

can you please number your answers so i can understand

Thanks for your help :)

Answer 1

1) Given: 7 dollars a month (fixed) ; 2 dollars per visit ; must spend less than 25 a month

7 + 2v < 25  (This is the inequality)
-7                  -7
         2v  < 18
        ÷2     ÷2
          v  < 9  

V can only equal to 1,2,3,4,5,6,7,and 8 to make the inequality true. Had it been less than or equal to, then V can have the value of 9. 

2. Given: 3 sets of 20 shots = a total of 60 shots
1st attempt : 13
2nd attempt : 18
3rd attempt : f (unknown)

average of 12 and 16 free throws:

(13 + 18 + f)/3 = 12
31 + x = 12*3
31 + f = 36
f = 36 - 31
f = 5

(13 + 18 + f)/3 = 16
31 + f = 16*3
31 + f = 48
f = 48 - 31
f = 17 

The 3rd attempt must be no less than 5 points and no more than 17 points to have an average of 12 and 16 free throws.

5 < f < 17

f can be equal to 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16. Not 5 and 17 because the problem states that it should be between the average of 12 and 16.