A-CED Questions

A-CED Questions

Literal Equations

Multiple Choice

A recreational softball league has 118 players register for the upcoming season. Each team in the league will have a maximum of 14 players, and each player can only be assigned to one team.

Which inequality can be used to calculate the minimum total number of teams, t, that the recreational softball league must have to assign all 118 players?

• $$118t\le14$$

• $$118t\ge14$$

• $$118\le14t$$

• $$118\ge14t$$

Multiple Choice

A landscaper services both residential and commercial sites. Each residential site requires an average of 2 hours of work and produces an average profit of $40 per service visit. Each commercial site requires an average of 3.5 hours of work and produces an average profit of $110 per service visit. In the upcoming week, the landscaper wants to produce more than $1,000 in profit and has up to 50 hours available to service sites.

Which system of linear inequalities represents this scenario, where r represents the total number of residential sites, and c represents the total number of commercial sites that the landscaper services?

• $$2r+3.5c<1,000$$ , $$40r+110c≥50$$

• $$2r+3.5c\le50$$ , $$40r+110c>1,000$$

• $$2r+3.5c>1,000$$ , $$40r+110c\le50$$

• $$2r+3.5c\ge50$$ , $$40r+110c<1,000$$

Multiple Choice

A concession stand has crates of bottled water to sell at a sporting event. Each crate holds 48 bottled waters and costs the concession stand $9.20.

If the concession stand wants to make exactly $34.00 profit per crate of bottled water, how much should customers be charged for each bottled water?

• $1.00 per bottled water

• $0.52 per bottled water

• $0.90 per bottled water

• $0.71 per bottled water

Multiple Choice

A piece of hardwood flooring has a width that is 8 inches less than its length, L. The piece of flooring is cut to decrease the width by 1 inch and decrease the length by 4 inches.

Which equation represents the area, H, of the piece of hardwood flooring after it is cut?

• $$H=L^2−7L$$

• $$H=L^2−8L$$

• $$H=L^2−11L+28$$

• $$H=L^2−13L+36$$

Multiple Choice

In a box of 20 marbles, there are 6 red marbles. There is 1 less green marble than red marbles, and the remaining marbles are blue.

How many blue marbles are in the box?

• 5 blue marbles

• 6 blue marbles

• 9 blue marbles

• 11 blue marbles

Multiple Choice

A band director wants to order music stands and music books.

- The band director has a budget of $850.

- Each music stand costs $25, and each music book costs $7.

- The band director needs at least 20 music stands and at least 40 music books.

If x represents the number of music stands, and y represents the number of music books, which system of inequalities represents this scenario?

• $$x≥20$$ , $$y≥40$$ , $$25x+7y≤850$$

• $$x≥20$$ , $$y≥40$$ , $$25x+7y≥850$$

• $$x≤20$$ , $$y≤40$$ , $$25x+7y≤850$$

• $$x≤20$$ , $$y≤40$$ , $$25x+7y≥850$$

Multiple Choice

Sienna and Wade open a lemonade stand in their neighborhood. On the first day, they sell x cups of lemonade and charge $1.50 per cup.

If it costs $0.45 to make each cup of lemonade, which equation represents the profit, P, that Sienna and Wade make on the first day?

• $$P=1.50+0.45x$$

• $$P=1.50−0.45x$$

• $$P=(1.50+0.45)x$$

• $$P=(1.50−0.45)x$$