SOLUTION: Dario has an arcade debit card with a $75 prepaid balance to use for the summer. Each time he plays a game he is charged 48 cents. The function b(g) = 75 − 0.48g models the amo

Algebra ->  Functions -> SOLUTION: Dario has an arcade debit card with a $75 prepaid balance to use for the summer. Each time he plays a game he is charged 48 cents. The function b(g) = 75 − 0.48g models the amo      Log On


   



Question 1203919: Dario has an arcade debit card with a $75 prepaid balance to use for the
summer. Each time he plays a game he is charged 48 cents. The
function b(g) = 75 − 0.48g models the amount of money Dario has on
his debit card after playing g games.
Select all of the constraints for this context.
Ⓐ b(g) ≥ 0
Ⓑ b(g) ≤ 75
Ⓒ b(g) ≤ 156
Ⓓ g ≥ 0
Ⓔ g ≤ 75
Ⓕ g ≤ 156

Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Think carefully about the function, the meaning, and the choices. Most of them are either wrong or make no sense.


(A) works.


But to be sure, understand that 0%3C=75-0.48g and see what that shows you.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answers: A, B, D, and F

Reason:

b%28g%29+%3E=+0 since the smallest balance is $0
b%28g%29+%3C=+75 since the largest balance is $75

We can combine those inequalities to write 0+%3C=+b%28g%29+%3C=+75

We must also require that g+%3E=+0. It makes no sense to have g as a negative number.

Solve b%28g%29+%3E=+0, aka 75-0.48g+%3E=+0, to end up with g+%3C=+156.25.
This tells us that the most games that can be played is 156.
Meaning we can say g+%3C=+156 since g is a whole number.

Notice how b(156) = 0.12 while b(157) = -0.36
There isn't enough money on the card to play the 157th game.

We can combine g+%3E=+0 (aka 0+%3C=+g) and g+%3C=+156 to get 0+%3C=+g+%3C=+156

In summary, we have these constraints
system%28b%28g%29+%3E=+0%2Cb%28g%29+%3C=+75%2Cg+%3E=+0%2Cg+%3C=+156%29
which represents choices A, B, D and F in that order.