PATTERNS AND FUNCTIONS WORD PROBLEMS

The function machines showed us that when a number goes in, it comes out changed by the rule or the function. There are many function patterns in real life.

Let us consider the examples given below.

Problem 1 :

At their Christmas fair, Middle Street School charges $1.50 for a gift wrapping service. Find the total cost of wrapped gift.

Solution :

Rule

Cost of wrapped gift = cost of unwrapped gift + $1.50

Cost of wrapped gift worth of $7 :

= Cost of unwrapped gift + $1.50

= 7 + 1.50

= $8.50

Cost of wrapped gift worth of $10 :

= Cost of unwrapped gift + $1.50

= 10 + 1.50

= $11.50

Cost of wrapped gift worth of $15 :

= Cost of unwrapped gift + $1.50

= 15 + 1.50

= $16.50

Cost of wrapped gift worth of $15 :

= Cost of unwrapped gift + $1.50

= 18 + 1.50

= $19.50

Problem 2 :

Complete the function table for the total cost of a day out at a fun park. You must pay an entry fee of $12 and purchase a wrist band for the amount of rides that you want to go on.

Solution :

Amount spent when 5 rides :

Total cost = Wrist band + $12

= $20 + $12

Total cost = $32

Amount spent when 6 rides :

Wrist band = $25

= $25 + $12

Total cost = $37

Amount spent when 7 rides :

Wrist band = $30

= $30 + $12

Total cost = $42

Amount spent when 8 rides :

Wrist band = $35

= $35 + $12

Total cost = $47

Problem 3 :

A dry cleaner charges $2 to iron a shirt.

a)  Write the rule for finding out the cost of ironing shirts when you know how many shirts

b) Complete the table, using the rule.

c) How much does it cost to have 12 shirts ironed ?

Solution :

a)  Cost = Number of shirts × $2

c)  Cost for 12 shirts :

Total cost = 12 x 2

= $24

Problem 4 :

Monica and Anna have a lemonade stand outside their house. For every liter of lemonade they make 4 cups to sell.

a) Write the rule for finding out how many cups are needed when you know how many liters have been made.

b)  Complete the table

c) How many will be needed if they have enough to make 12 liters of lemonade ?

Solution :

a)

Number of cups they can make = quantity in liters x 4

b) 

c) For 12 liters of lemonade,

Cups = 12 × 4

= 48

48 cups are needed.

Problem 5 :

Complete the function table for the total cost of lunch at a school canteen. Students pay $2.40 for a sandwich and then choose what else they would like. Work out the total cost of lunch for each option.

Rule :

Total lunch = Lunch option + $2.40

Solution :

Total cost when drink is in it :

= Drink + $2.40

= 0.80 + $2.40

= $3.20

Total cost when fruit is in it :

= Fruit + $2.40

= 0.95 + $2.40

= $3.35

Total cost when yogurt is in it :

= Yoghurt + $2.40

= $1.10 + $2.40

= $3.50

Total cost when ice block is in it :

= Ice block + $2.40

= $1.50 + $2.40

= $3.90

Problem 6 :

5F have fitness every Thursday afternoon for 30 minutes. Each week they complete a fitness activity and then play running games. Work out how much time is left for games each activity.

Rule

Time left for games = 30 minutes - length of time of activity

Solution :

Time left for games = 30 - 10

= 20 minutes

Time left for games = 30 - 12

= 18 minutes

Time left for games = 30 - 15

= 15 minutes

Time left for games = 30 - 16

= 14 minutes

Problem 7 :

At cinema, the lollies are sold by weight 1 scoop costs 50 cents.

a)  Write the rule to find out the cost of the lollies when you know how many scoops.

b) Using the rule, complete the table.

c)  How many scoops of lollies can i get for $10.

Solution :

Rule:

Cost = scoops of lollies × 50 c

Cost = scoops of lollies × 0.5

c) Amount to be paid = $10

Number of scoops x 0.50 = 10

Number of scoops = 10/0.50

o, the required number of scoops = 20.