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

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) (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 and see what that shows you.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answers: A, B, D, and F

Reason:

since the smallest balance is $0
since the largest balance is $75

We can combine those inequalities to write

We must also require that . It makes no sense to have g as a negative number.

Solve , aka , to end up with .
This tells us that the most games that can be played is 156.
Meaning we can say 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 (aka ) and to get

In summary, we have these constraints

which represents choices A, B, D and F in that order.

RELATED QUESTIONS
Dario has an arcade debit card with a $75 prepaid balance to use for the summer. Each... (answered by mananth,ikleyn)
Charlie has a $30 smoothie gift card. Each time he uses the card to buy a smoothie, $2 is (answered by TimothyLamb,MathTherapy)
Please help I When Mr. Selig took over as president of Century several years ago, the use (answered by richwmiller)
Q: A game of �Quick Draw� is played in a certain casino. In the game, a player chooses a (answered by solver91311)
Bobs big bagels offers prepaid cards and has the special showing Carol has a $50 card... (answered by addingup)
Guy has a gift card that he uses to buy video games. Each game costs $7, and after buying (answered by josgarithmetic)
Trey has a deck of 10 cards numbered 1 through 10. He is playing a game of chance. This... (answered by Glaviolette,math_tutor2020)
Mr.chang has $10,000 in a savings account. He wants to pay of $3500 credit card purchase. (answered by Boreal,MathTherapy)
1. Andrew buys a 50$ phone card. He is charged $.25 per minute for the calls that he... (answered by solver91311)