Question

Baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each. Ticket prices for the upper deck are 75% of the cost of tickets for the lower deck.
Which inequality represents all possible combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for no more than $800?
A) 42x + 56y ≤ 800
B) 42x + 31.5y ≤ 800
C) 42x + 56y > 800
D) 42x + 31.5y > 800

Answer 1

X=42$
y=0.75*42$=31.5$

42*42+56*31.5=3528
42*42+31.5*31.5=2756.25
C and D are correct inequalitys

Answer 2

If tickets for the upper deck are 75% of the cost of tickets for the lower deck and lower deck tickets are $42, then tickets for the upper deck $31.50 each. Therefore the answer cannot be A or C, because both of those options misstate the cost of the upper deck ticket. The answer also cannot be D, because it expresses the inequality when the combined number of tickets is greater than $800, which is not what was asked for. The correct answer is B. 42x + 31.5y ≤ $800. This gives the correct price for upper deck tickets and expresses the correct inequality.