A shop sells balloons in packs of r. A class buys 5 such packs, uses 12 balloons to decorate the hall, and has 63 balloons left. How many balloons are in each pack?
There are 15 balloons in each pack.
Ans: 15
How to solve it
Call the unknown number r: each pack has r balloons, and there are 5 packs.
Draw the 63 balloons left as one strip, then put the 12 used back on in purple.
Add to find the whole: 63 plus 12 is 75 balloons.
The same whole is 5 packs of r, so 5 r and 75 are the same amount.
Divide to find one pack: r is 75 divided by 5, which is 15 balloons.
The total is also 5 times r, one r in each pack. So 5 r and 75 are the same amount. So r is 75 divided by 5, which is 15.
Practice questions with worked solutions
Question 1 is free to try. The other 10 open in the free trial, each with its full working.
What are the steps for solving simple equations in P6 algebra?
An equation says two amounts are the same, and solving it finds the value of the letter.
What your child learns here
An equation says two amounts are the same, and solving it finds the value of the letter. The Primary 6 syllabus keeps these simple: whole number coefficients, one letter, no brackets.
Write an equation from a story or a bar model, with the letter standing for the unknown number.
Tidy each side first, so that collecting like terms or working out a plain sum comes before any undoing.
Undo the operations in the reverse order: put back what was taken off, then divide by the number in front of the letter.
Check the answer by substituting it back into the original equation.
Know that a short story may also be solved by 'undoing the story' in plain arithmetic, and that the equation is the dependable route when the story gets long.
Does the answer make sense?
Every answer on this page is a whole number, and it is smaller than the largest amount the question gives, because it is only one part of that amount. An answer with a fraction or a decimal, or one above that largest amount, tells your child to undo the steps again in reverse order.
How to practise these questions
The Basic questions train turning a bar model into an equation and tidying it before dividing. Intermediate questions add two-step equations, where the last operation done is the first one undone. In Challenge questions the letter sits at one end of a chain and the quantity asked for is at the other end, so solving for the letter is only halfway. When an equation will not balance, read the written step-by-step solution together.
Questions parents ask
What kind of equations does a P6 child solve? The Primary 6 syllabus covers simple linear equations involving whole number coefficients only. In practice that means one letter with a whole number in front of it, such as 4n + 6 = 30.
Does my child have to write an equation, or can they just work backwards? For a short story, working backwards in plain arithmetic reaches the same answer, and our lesson treats it as a valid route. As the story gets longer, an equation keeps every step in view, so it helps to know both.
Should my child use the balance method to solve equations? Our lessons solve by undoing the operations in reverse order, written as plain arithmetic, and do not draw a balance. If your child's school uses a balance picture, it reaches the same answer.
