You are taking a test in which items of type a are worth 10 points and items of type b are worth 15 points. it takes 3 minutes for each item of type a and 6 minutes for an item of type b. total time allowed is 60 minutes, and you may answer more than 16 questions. assuming all your answers are correct, how many items of each type should you answer in order to get the best score?

The best score is 200 points, answering 20 items of type A.

Step-by-step explanation:

Let the following variables be:

x: items of type A

y: items of type B

The first condition is that it takes 3 minutes for each item of type A and 6 minutes for an item of type B. Total time allowed is 60 minutes. The equation would be:

Furthermore,  you may answer more than 16 questions. The second equation would be:

We show the plots of both equations in the attached pictures we find 3 critical points:

P₁ (16,0); P₂ (12,4); P₃ (20,0)

The score of the test would be:

S= 10x + 15y

We evaluate the points

P₁ (16,0)

S(16,0)= 10×16 + 15×0=160 points

P₂ (12,4)

S(16,0)= 10×12 + 15×4=180 points

P₃ (20,0)

S(20,0)= 10×20+ 15×0=200 points

answer:

24 and 26

step-by-step explanation:

x = smaller

x+2 = larger

their sum, x+(x+2), is greater than, > , 98 decreased by, -, twice the

larger, 2(x+2).

so:

x+(x+2) > 98-2(x+2)

  x+x+2 > 98-2x-4

  2x+2 > 94-2x

  2x+2x > 94-2

    4x > 92

      x > 23

since x is the smaller, it must be greater than 23,

and the larger, x+2, must be 25 or larger.

the smallest two such consecutive even integers are 24 and 26.