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8.10 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 spend 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

Tennis coach Luigi has 5 balls left. To ensure he has enough for the next training session, he orders one new pack of balls for each of his y students.

a

If the new tennis balls come in packs of 4, write an algebraic expression for the total number of tennis balls Luigi will have.

b

Find the number of tennis balls Luigi will have if he coaches 7 students.

12

Sarah has 14 cookies in her cookie jar. Her 2 children each eat a cookie every day.

a

Write an algebraic expression for the number of cookies left in the jar after y days.

b

Are the number of cookies decreasing by the same amount each day?

13

Vanessa has \$700 in her bank account. She only uses the account to pay her mobile phone bill each month.

a

If each monthly bill is \$14, write an algebraic expression for how much Vanessa has in her account after c months.

b

Find the amount of money she will have in her account after she pays her bill for 4 months.

14

Sally attends a dessert festival. Each ice cream costs \$6 and each milkshake costs \$8.

a

If Sally buys c ice creams and m milkshakes, write an algebraic expression for the total cost.

b

How much would two ice creams and one milkshake cost?

c

Using algebra, how much would c ice creams and no milkshakes cost?

15

Laura has a piggy bank in which she collects 20c and 50c coins. After some time, she loses track of how many coins are in the piggy bank.

a

Let m represent the number of 20c coins and n represent the number of 50c coins. Write an algebraic expression for the total value of Laura’s coins in cents.

b

Laura breaks her piggy bank and discovers that she has thirteen 20c and twenty-seven 50c coins. Find the total value of these coins in dollars.

16

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.

17

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?

18

Fred likes to go kayaking. He takes his boat down to the lake which is 400 m away from his house.

  • After 1 minute of paddling he is 490 m away from his house

  • After 2 minutes of paddling he is 580 m away from his house

  • After 3 minutes of paddling he is 670 m away from his house

a

Fred paddles for n minutes in total. Write an algebraic expression for the distance from his house at this time.

b

How far does Fred travel in the kayak per minute?

c

Is Fred is paddling at a constant pace for the first n minutes?

d

If Fred kayaks for 10 minutes, how far does he travel from his house altogether?

19

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.

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MA4-8NA

generalises number properties to operate with algebraic expressions

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