Linear Word Problems Standard Form

Two farmers use combines to harvest corn from their fields. One farmer can harvest 600 acres of corn per day, and the other farmer can harvest 1000 acres of corn per day. They harvested 9800 acres of corn total. Which equations could represent this situation? Choose all that apply.

• 600x + 1000y = 9800

• 1000x + 600y = 9800

• y = 6/10x + 9800

• y = 10/6x + 9800

A football team scores 63 points. All of the points come from field goals (x) worth 3 points and touchdowns (y) worth 7 points. Write an equation in standard form that represents this situation. Then convert it to slope-intercept form. Select the correct standard form and slope-intercept form.

• 3x + 7y = 63

• 7x + 3y = 63

Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance y after x hours.

• y = 40x + 65

• y = 65x + 40

• 40x + 65y = 105

• y - 40 = 65(x - 0)

The booster club made $708 on homecoming T-shirt sells. Small t-shirts cost $12 while large t-shirts cost $14. If x is small t-shirts and y is large t-shirts, what equation represents this.

• 12x + 14y = 708

• 14x + 12y = 708

• 708x + 14y = 12

• 12x + 708y = 14

Which of the following situations could be descried by the equation y= -25x + 120

• There are 120 people in the football stadium, and 25 more are entering each hour.

• A plumber charges $25 for a house call and $120 per hour.

• A teacher has 120 students. Her third period has 25 students

• There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

• y=15x

• y=15x+80

• y=x+15

• y=80x+15

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation for C, the total cost, to rent the boat for h hours.

• h = 2C + 15

• C = 15h + 2

• h = 15C + 2

• C = 2h + 15

What is standard form of a line?

• y = mx + b

• Ax + By = C

• y - y1 = m(x - x1)

• y = Ax + By

Which equation is written in STANDARD form?

• y = 1/2x + 2

• y - 3 = -5(x + 2)

• -7x + 2y = 9

• 3x + 2 = y