6.06 Solving contextual problems with algebra
Adam sells chocolates to raise money for charity. Each chocolate costs \$6.
If Adam sells q chocolates, write an algebraic expression for the amount of money he raises.
How much do 4 chocolates cost?
How much do 5 chocolates cost?
Is it possible to raise exactly \$13 if Adam sells chocolates at \$6?
Valentina's hens can produce 5 eggs each day.
If Valentina collects the eggs from her hens for y days, write an algebraic expression for the total number of eggs.
Find the number of eggs Valentina will have after 30 days.
John breeds dogs for sale. Each of his d dogs gives birth to p puppies.
Write an algebraic expression for the total number of puppies.
Can the value of p be a fraction?
If he has 3 dogs, find the total number of puppies.
Judy has 72 pencils, which she shares evenly among the students in her class.
If there are q students in her class, write an algebraic expression for the number of pencils given to each student.
If there are 18 students in the class, how many pencils does each student receive?
If there are 36 students in the class, how many pencils does each student receive?
As the number of students in the class increases, does the number of pencils each student receives increase or decrease?
At John's birthday party, cake slices are shared evenly among his 8 guests.
If John shares x slices, write an algebraic expression for the number of slices given to each guest.
If John shares 32 cake slices, find the number of slices given to each guest.
Kenneth uses a watering can to give each of his plants an equal amount of water.
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.
As n increases, do the plants receive more or less water?
Robert visits a carnival that costs \$5 to enter, and each ride costs \$1 per person.
If Robert decides to go on b rides, write an algebraic expression for the total amount he spends at the carnival.
If Robert goes on 6 rides, calculate the amount of money he spends in total.
Ben has 241 GB of available space on an external hard drive. He decides to transfer his files to this drive.
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.
Find the space left if Ben transfers 16 GB in total.
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.
If the bus trip takes n minutes, write an algebraic expression for the total time it takes Amelia to get to school.
Yesterday the bus trip took 15 minutes. Find the total time it took for Amelia to get to school yesterday.
In a Year 7 class, students are either twelve years old or thirteen years old.
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.
If there are 4 twelve year-old and 16 thirteen year-old students, find the number of students are in the class.
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.
If the number of birds continues to follow the pattern, find the number of birds that Valerie will see on the fourth day.
If the pattern continues, write an algebraic expression for the number of birds Valerie sees on the x th day.
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
If the tap stops leaking after a hours, write an algebraic expression for the water level in the bucket at this time.
Is the water level increasing by the same amount each hour?
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
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.
Write an algebraic expression for the number of 1 cm^2 are in a square with a side length of h cm.
The perimeter, P, of a rectangle is given by the formula P=2l+2w, where l is the length and w is the width.
Find the value of w that makes the statement true.
Describe the rectangle that corresponds to the statement.
A racing car starts the race with 80 litres of fuel. From there, it uses fuel at a rate of 2 litres per minute.
Complete the table below:
| \text{Number of minutes passed} | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Amount of fuel left in tank} | 80 |
Write an algebraic rule relating the number of minutes passed \left( x \right) and the amount of fuel left in the tank.
After how many minutes, x, will the car need to refuel (i.e. when there is no fuel left)?
The temperature of a beaker of water increases by 4 \degree \text{C} each minute.
Complete the table below:
| \text{Time in minutes} | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Temperature in} \degree \text{C} | 5 |
Write an algebraic rule relating the time, x and the temperature.
What would the temperature have been at 10 minutes?
Pencils cost \$2 and pens cost \$3.
Write an expression for the total cost of x pencils and y pens.
Find the total cost of 5 pencils and 6 pens.
Lara spends a total of \$35 on four pencils and a number of pens. How many pens did she buy?
Marge is looking at accommodation prices in Paris. One particular hotel charges \$200 for the first night, and then \$150 for every additional night.
If Marge stays n nights, write an algebraic rule to find the cost of her stay.
Find the cost of Marge staying for:
3 nights
5 nights
Marge has a budget of \$1400. Find the number of nights she can afford to stay.