Linear Equations from Story Problems Quiz

Jamie is buying pencils. Each pencil costs $0.50, and there is a fixed fee of $1.00 for packaging. Which equation models the total cost $C$, in dollars, if Jamie buys $p$ pencils?

• C = 0.5p

• C = 1p + 0.5

• C = 0.5p + 1

• C = p + 0.5

A plant was 10 cm tall two weeks ago and grew to 16 cm tall this week. Assume the plant grows at a constant rate. Which equation models the height, $H$, of the plant in centimeters after $w$ weeks since the measurement two weeks ago?

• H = 3w + 10

• H = 2w + 6

• H = 6w - 10

• H = w + 16

A toy company can produce either 4 action figures or 3 dolls in one hour. They have a total of 24 hours to produce toys. Which equation represents this production constraint?

• 4x + 3y = 24

• 3x + 4y = 24

• 4x + y = 24

• 3x + y = 24

A car rental company charges a daily fee of $20 plus $0.15 per mile driven. Which equation represents the total cost $C$, in dollars, for renting the car for one day and driving $m$ miles?

• C = 0.15m

• C = 20 + 15m

• C = 0.15m + 20

• C = 15m + 0.20

At 3 p.m., the temperature was 70°F, and by 8 p.m., it had dropped to 55°F. Assume the temperature decreased at a constant rate. Which equation models the temperature $T$, at any time $t$, in hours since 3 p.m.?

• T = -3t + 79

• T = -3t + 70

• T = -5t + 70

• T = -3t + 75

A juice company mixes two types of juice to create a blend. Orange juice costs $2 per gallon, and apple juice costs $3 per gallon. The company wants to produce a blend that costs exactly $50. Which equation represents the situation?

• 2x + y = 50

• x + 3y = 50

• 2x + 3y = 50

• x + 2y = 50

Maria earns $10 per hour babysitting, and she received an additional $15 as a holiday bonus. Which equation models her total earnings $E$, if she works $h$ hours?

• E = 10h

• E = 10h + 15

• E = 15h + 10

• E = 15h

A hot air balloon is at an altitude of 300 feet after 2 minutes and rises to 450 feet after 5 minutes. Assume it rises at a constant rate. Which equation models the altitude $A$, in feet, after $t$ minutes?

• A = 50t + 200

• A = 45t + 300

• A = 30t + 300

• A = 50t + 300

A school fundraiser sells boxes of cookies and chocolates. A box of cookies sells for $5, and a box of chocolates sells for $8. They want to raise at least $200. Which equation represents this fundraising goal?

• 5x + y = 200

• x + 8y = 200

• 5x + 8y = 200

• x + y = 200

A cell phone company offers a plan that costs $20 per month plus $0.05 for each text message sent. Which equation models the total monthly cost $C$, if $t$ text messages are sent?

• C = 0.05t + 20

• C = 20 + 5t

• C = 5t + 20

• C = 0.5t + 20