NC.M1.A-REI.6 Systems of Equations

A rectangle has a perimeter of 74 centimeters. The length of the rectangle is 5 centimeters less than twice the width. What is the area of the rectangle, in square centimeters?

• 294

• 322

• 336

• 368

Matthew and Kevin each begin filling pools at the same time.

Matthew fills his pool at a rate of 6 gallons per minute.

Kevin’s pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.

How many minutes pass before both pools have the same amount of water?

• 300

• 100

• 50

• 33

Mrs. Williams bought cans of pears and cans of mixed fruit.

She bought a total of 7 cans at a cost of $21.50.

Each can of pears cost $3.20, and each can of mixed fruit cost $2.90.

How many cans of mixed fruit did Mrs. Williams purchase?

Halle traveled 20 miles in 3 hours.

Halle walked part of the distance at a speed of 4 miles per hour.

Halle rode her bicycle for the remaining distance at a speed of 12 miles per hour.

How many hours did Halle spend walking?

Which system of equations would have no solution?

• Danna rents a car for 1 day.

• Danna rents a car for 2 days.

• Danna rents a car for 3 days.

• Danna rents a car for 5 days.

A club will create T-shirts for a fundraiser. The club members need to compare the cost of creating the T-shirts between two companies. Company A charges $30 for setup, plus $5 per T-shirt. Company B charges $15 for setup, plus $7 per T-shirt.

 Which option below best interprets the results from the graphic solution of these paired equations?

• For orders less than or equal to 7 shirts, the cost using Company A is less.

• For orders less than or equal to 8 shirts, the cost using Company A is less.

• For orders less than or equal to 7 shirts, the cost using Company B is less.

• For orders less than or equal to 8 shirts, the cost using Company B is less.

Farmer Darien has 300 acres of land and $117,335 available to produce corn and soybeans. Each of these acres is used to produce one of these two crops. It costs the farmer $349 per acre to produce soybeans and $444 per acre to produce corn. If all the money is used for these two crops, how many acres of soybeans are produced by Farmer Darien?

• 133

• 148

• 150

• 167

An apartment building contains 100 units. The one-bedroom units rent for $495 per month and the two-bedroom units rent for $600 per month. When all the units are rented out, the total monthly rent paid by the tenants is $55,275. How many two-bedroom apartments are there?

• 45

• 50

• 55

• 66