Function Modeling Word Problems

A local donut shop charged $6.50 for a dozen and provided a coupon in the newspaper for $1.50 off an order. Since the donut shop has gained popularity they have changed their coupon which now provides a discount of only half their original coupon's value. What is the equation that represents the value of a customer's order who uses the new coupon with their order?

• y = 6.50x - 0.75

• y = 6.50x + 0.75

• y = 6.50x - 1.50 - 0.75

• y = 5x - 0.75

Heather is a hairdresser and her customers pay $5 to reserve an appointment time and $12 for every hour Heather works on their hair style. As a back to school special she offers to lower her price per hour by $5. What equation represents the total amount paid to Heather, y, after x hours of hair styling?

• y = 5 + 12x

• y = 12x

• y = 7x + 5

• y = 12x + 12

Randy charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents so as a result he must increase the rate of change by $25 to ensure his profits are not harmed. What equation best represents how much his tenants will now have to pay?

• y = 425x + 600

• y = 425 + 600x

• y = 400x + 625

• y = 400 + 625x

Valley Video charges a $15 annual fee plus $3 per movie for rentals. Last year, Jennifer spent $99 at the video store. How many movies did she rent? Write the linear equation and solve for the number of movies.

• 15x + 3x = 99    and 6 movies

• 15x + 3 = 99 and 6 movies

• 3x + 15 = 99 and 28 movies

• 3x + 99 = 15 and 28 movies

Which function best models the height and speed of throwing a ball in the air?

• Linear

• Quadratic

• Exponential

Pick a function that best models the following situation: A speed of a rollercoaster from start to finish. 

• Exponential

• Linear

• Quadratic

• Neither

Karen earns $28.50 for working six hours. If the amount m she earns varies directly with h the number of hours she works, how much will she earn for working 10 hours?

• $47.50

• $17.10

• $54.75

• $45.55

The time to complete a project varies inversely with the number of employees.
If 3 people can complete the project in 7 days, how long will it take 5 people?

• 12 days

• 4.2 days

• 6.2 days

• 10 days

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

•  length = 26 yd, width = 21 yd

• length = 21 yd, width = 26 yd 

• length = 21 yd, width = 16 yd 

• length = 16 yd, width = 21 yd

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

• 8 painters

• 10 painters

• 9 painters

• 11 painters