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Australia
Year 7

6.06 Solving contextual problems with algebra

Worksheet
Problem solving with algebra
1

Adam sells chocolates to raise money for charity. Each chocolate costs \$6.

a

If Adam sells q chocolates, write an algebraic expression for the amount of money he raises.

b

How much do 4 chocolates cost?

c

How much do 5 chocolates cost?

d

Is it possible to raise exactly \$13 if Adam sells chocolates at \$6?

2

Valentina's hens can produce 5 eggs each day.

a

If Valentina collects the eggs from her hens for y days, write an algebraic expression for the total number of eggs.

b

Find the number of eggs Valentina will have after 30 days.

3

John breeds dogs for sale. Each of his d dogs gives birth to p puppies.

a

Write an algebraic expression for the total number of puppies.

b

Can the value of p be a fraction?

c

If he has 3 dogs, find the total number of puppies.

4

Judy has 72 pencils, which she shares evenly among the students in her class.

a

If there are q students in her class, write an algebraic expression for the number of pencils given to each student.

b

If there are 18 students in the class, how many pencils does each student receive?

c

If there are 36 students in the class, how many pencils does each student receive?

d

As the number of students in the class increases, does the number of pencils each student receives increase or decrease?

5

At John's birthday party, cake slices are shared evenly among his 8 guests.

a

If John shares x slices, write an algebraic expression for the number of slices given to each guest.

b

If John shares 32 cake slices, find the number of slices given to each guest.

6

Kenneth uses a watering can to give each of his plants an equal amount of water.

a

If his watering can contains m mL of water and he has n plants, write an algebraic expression for how much water is given to each plant.

b

As n increases, do the plants receive more or less water?

7

Robert visits a carnival that costs \$5 to enter, and each ride costs \$1 per person.

a

If Robert decides to go on b rides, write an algebraic expression for the total amount he spends at the carnival.

b

If Robert goes on 6 rides, calculate the amount of money he spends in total.

8

Ben has 241 GB of available space on an external hard drive. He decides to transfer his files to this drive.

a

If the transferred files have a total size of x GB , write an algebraic expression for the amount of space left on the external drive.

b

Find the space left if Ben transfers 16 GB in total.

9

To get to school, Amelia walks for 9 minutes to the bus stop and waits 2 minutes for the bus to arrive. She rides the bus for the rest of the way to school.

a

If the bus trip takes n minutes, write an algebraic expression for the total time it takes Amelia to get to school.

b

Yesterday the bus trip took 15 minutes. Find the total time it took for Amelia to get to school yesterday.

10

In a Year 7 class, students are either twelve years old or thirteen years old.

a

If there are k twelve year-old and m thirteen year-old students, write an algebraic expression for the total number of students in the class.

b

If there are 4 twelve year-old and 16 thirteen year-old students, find the number of students are in the class.

11

Valerie places a bird feeder in her garden. That day, she sees 3 birds use the feeder. The next day she sees 6 birds, and on the third day she sees 9 birds.

a

If the number of birds continues to follow the pattern, find the number of birds that Valerie will see on the fourth day.

b

If the pattern continues, write an algebraic expression for the number of birds Valerie sees on the x th day.

12

Water is dripping from a tap into a large bucket, so that:

  • After 1 hour, the water level in the bucket is 5 cm

  • After 2 hours the water level is at 10 cm

  • After 3 hours the water level reaches 15 cm

a

If the tap stops leaking after a hours, write an algebraic expression for the water level in the bucket at this time.

b

Is the water level increasing by the same amount each hour?

13

Kathleen cuts squares from 1 cm grid paper:

  • The first square is 2 \text{ cm} \times 2 cm and has an area that contains four 1 cm^2 pieces

  • The second square is 3 \text{ cm} \times 3 cm and has an area that contains nine 1 cm^2 pieces

  • The third square is 4 \text{ cm} \times 4 cm and has an area that contains sixteen 1 cm^2 pieces

a

If the pattern continues, find the number of 1 cm^2 pieces that fit in a square that is 5 \text{ cm} \times 5 cm.

b

Write an algebraic expression for the number of 1 cm^2 are in a square with a side length of h cm.

14

The perimeter, P, of a rectangle is given by the formula P=2l+2w, where l is the length and w is the width.

a
Find the perimeter of a rectangle if l=10 and w=6.
b
Consider the statement: 50=2\times 18 +2w
i

Find the value of w that makes the statement true.

ii

Describe the rectangle that corresponds to the statement.

15

A racing car starts the race with 80 litres of fuel. From there, it uses fuel at a rate of 2 litres per minute.

a

Complete the table below:

\text{Number of minutes passed} 01234
\text{Amount of fuel left in tank} 80
b

Write an algebraic rule relating the number of minutes passed \left( x \right) and the amount of fuel left in the tank.

c

After how many minutes, x, will the car need to refuel (i.e. when there is no fuel left)?

16

The temperature of a beaker of water increases by 4 \degree \text{C} each minute.

a

Complete the table below:

\text{Time in minutes} 01234
\text{Temperature in} \degree \text{C} 5
b

Write an algebraic rule relating the time, x and the temperature.

c

What would the temperature have been at 10 minutes?

17

Pencils cost \$2 and pens cost \$3.

a

Write an expression for the total cost of x pencils and y pens.

b

Find the total cost of 5 pencils and 6 pens.

c

Lara spends a total of \$35 on four pencils and a number of pens. How many pens did she buy?

18

Marge is looking at accommodation prices in Paris. One particular hotel charges \$200 for the first night, and then \$150 for every additional night.

a

If Marge stays n nights, write an algebraic rule to find the cost of her stay.

b

Find the cost of Marge staying for:

i

3 nights

ii

5 nights

c

Marge has a budget of \$1400. Find the number of nights she can afford to stay.

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Outcomes

ACMNA176

Create algebraic expressions and evaluate them by substituting a given value for each variable

ACMNA177

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions

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