Algebra & Equations (Worded Problems)
A streaming service charges a sign-up fee of fifteen dollars and nine dollars per month. What is the total cost after six months?
The total cost after six months is sixty-nine dollars.
A recipe uses four cups of flour to make sixteen muffins. If you only have two cups of flour, how many muffins can you make?
You can make eight muffins with two cups of flour.
A right-angled triangle has one side that is three metres long and another side that is four metres long. What is the length of the longest side?
Five metres – found using Pythagoras' theorem.
A fair coin is flipped once. What is the chance of it landing on heads?
The chance is one out of two.
Katie puts three hundred dollars into a savings account that earns simple interest of three percent per year. How much interest will she have after four years?
The interest after four years is thirty-six dollars.
The sum of two numbers is thirty-five, and their difference is seven. What are the two numbers?
The two numbers are twenty-one and fourteen.
A cyclist travels sixty kilometres in three hours. What is their average speed in kilometres per hour?
The average speed is twenty kilometres per hour.
A ladder is leaning against a wall. The base of the ladder is two metres away from the wall, and the ladder reaches a height of four point eight metres on the wall. What is the length of the ladder?
Approximately five point two metres – Pythagoras' theorem.
A bag contains five red balls and five blue balls. One ball is drawn, then replaced, and another is drawn. What is the chance both balls are red?
The chance both are red is one out of four.
A phone costs one thousand dollars. You can pay four equal instalments after paying a deposit of two hundred dollars. What is the value of each instalment?
Each instalment is two hundred dollars.
A number is squared, and then five is subtracted from it. The result is fifty-nine. What is the original number?
The original number is eight.
A water tank fills at a constant rate. After five hours, it has filled two hundred and fifty litres. How much water will be in the tank after eight hours?
After eight hours, the tank will have four hundred litres of water.
A flagpole casts a shadow that is five point two metres long. If the angle of elevation from the tip of the shadow to the top of the flagpole is thirty degrees, how tall is the flagpole?
Approximately three metres – used tangent ratio.
A class has ten boys and fifteen girls. One student is chosen at random. What is the chance it is a girl?
The chance is three out of five.
A television is bought for twelve hundred dollars and loses ten percent of its value each year. What will it be worth after two years?
After two years, the television will be worth approximately nine hundred and seventy-two dollars.
A shop sells notebooks for four dollars each and pens for two dollars each. If a customer spends a total of thirty dollars, how many of each item could they have bought?
The customer could have bought combinations such as four notebooks and seven pens, or other combinations that total thirty dollars.
A car uses forty litres of fuel to travel three hundred kilometres. How much fuel will it use to travel four hundred and fifty kilometres at the same rate?
The car will use sixty litres of fuel to travel four hundred and fifty kilometres.
A cable is attached from the top of a building to a point on the ground ten metres away from the base. If the cable makes an angle of seventy degrees with the ground, find the height of the building.
Approximately nine point four metres – used sine ratio.
A dice is rolled three times. How do you work out the chance of getting exactly two sixes?
You use the probability rule for repeated trials, combining the chances of two sixes and one other number.
A loan of five thousand dollars is taken with interest charged monthly. Describe how the total repayment changes depending on the number of months.
The more months the loan is spread across, the smaller each monthly repayment will be, but the total repayment amount may increase due to the interest adding up.
A company’s profit depends on how many items they sell. Their profits increase at first and then decrease. How can you find the number of items that gives the highest profit?
You find the number of items that gives the highest profit by identifying the turning point of the profit rule, which is usually found by looking for the maximum point on a graph or using a method like completing the square.
A factory produces twelve hundred cans in eight hours with six workers. How many cans would the factory produce in the same amount of time if nine workers were working at the same rate?
The factory would produce one thousand eight hundred cans with nine workers in eight hours.
A triangle has two sides that are eight metres and six metres long, and the angle between them is forty-five degrees. Calculate the length of the third side using the cosine rule.
Approximately five point eight metres – used cosine rule.
A test was marked out of one hundred. The scores of five students were recorded. How can you calculate the average, and how does adding a sixth score that is much higher change it?
To find the average, add all the scores and divide by the number of students. Adding a much higher sixth score will increase the average.
Leo invests three thousand dollars at compound interest. Explain how compound interest grows differently compared to simple interest over five years.
Compound interest grows faster over time than simple interest because interest is also earned on previous interest.