MathsFreePrintable

Applied Algebra Adventure

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Applied Algebra Adventure

Read each question carefully. Show your working for calculation questions. Use dollars (NZ$) where needed.

Linear relationships in context

1.A bike hire shop charges a fixed fee of NZ$8, then NZ$4.50 for each hour hired. Which rule gives the total cost C for h hours?

C = 8h + 4.50
C = 4.50h + 8
C = 12.50h
C = 8 + 4.50

2.For the linear rule y = 6x + 2, identify the gradient.

3.A streaming service charges NZ$14 each month plus NZ$1.20 for each film rented. Complete the table to find the monthly cost for 0, 5, 15 and 30 rentals.

Number of films rented: 0 | 5 | 15 | 30

Monthly cost (NZ$): ______ | ______ | ______ | ______

4.Write a rule for the streaming service’s monthly cost C when f films are rented.

Use algebra to solve problems

5.A community fair pays NZ$32 to hire a game stall and earns NZ$4 for each game played. How many games must be played to earn at least NZ$180 after paying the hire cost? Show an inequality and solve it.

6.A model predicts the air temperature y°C at an altitude of x kilometres using y = -1.5x + 19. What temperature does it predict at sea level?

7.A pottery studio charges NZ$45 to join a workshop, plus NZ$12 for each clay item made. One customer pays NZ$141 altogether. Write an equation and find how many clay items they made.

Create and test a linear rule

8.Invent a real-world situation that can be modelled by a linear rule. Describe what x and y represent, then write your rule in the form y = mx + b.

9.Using your rule from the previous question, choose three x-values and calculate the matching ordered pairs (x, y). Show the substitution for each pair.