9. Growth in Numbers within Image Multiples
This type of question is similar to algebra questions in that you are often required to form algebraic equations in order to find the answer. You will know you are dealing with this type of question in the exam if the question is structured similar to the below.
How many black socks are there in a drawer with 88 socks if there are 1/3 as many white socks as black socks? Assume that there are only black and white socks in a drawer.
This type of question requires the student to use a whole variety of skills such as basic arithmetic, decimals, fractions and percentages. Many of these questions ask you to identify a mathematical relationship from what is given to you and to use that relationship to find the unknown number.
So…how do you solve this type of question in the exam? It is easiest to use visual analysis – that is, draw out the question and find the answer from that. Below is a step-by-step guide to completing visual analysis.
| Steps | Proposed Action |
|---|---|
| Step One | Read the question carefully. Key words such as 'twice as much' and 'if… will be equal to' reveal important clues that will help you form pictures in your head. |
| Step Two | Extract the necessary information. Represent unknowns as variables, such as x,y,z. Illustrate the numbers in terms of pictures. For example, draw 5 balloons. If person 2 has twice as many balloons as person 1, draw a question mark inside the balloon to represent the unknown amount and write "x 2" to suggest that you need to multiply the question mark balloon by 2 in order to get the number of balloons person 2 has. |
| Step Three | List out the information you have extracted one by one. Form a relationship between the pictures by drawing arrows. Remember to direct the arrows towards the subject of the question. In other words, make sure the pictures lead to the final answer. |
| Step Four | Solve the answer by following the arrows. Remember to convert the answer to the unit required, for example, kilograms, kilometres etc… as needed. |
Now…let's look at an example.
If Amanda had 5 cents more she would have twice as much as Albert. If she had 4 cents less, she would have the same amount. How many cents does Amanda have?
| Steps | In Action… |
|---|---|
| Step One | Read the question. |
| Step Two | Extract the necessary information.If Amanda had 5 cents more she would have twice as much as Albert.  If Amanda had 4 cents less she would have the same amount as Albert. 
|
| Step Three | Form a relationship between the pictures.I have done so already in step 2. Now you just put them together, using statement 2. 
|
| Step Four | Solve.You will find Amanda's amount equal to 13 cents. This is because we isolate out Amanda's amount by rearranging the equation. Remember, we are trying to find Amanda's amount. Rearrange the equation by making Amanda's amount the subject."Amanda's Amount" + 5 = (2 x "Amanda's Amount") – 8When you solve for this, the answer is 13.You should refer to a mathematics textbook if you don't know how to rearrange equations. |
Now, let's do some example questions:
Example 1
Jacob got 18 marks in a test. If Maria had gotten 2 more marks then she would have twice as many marks as Jacob.
How many marks did Maria get?
A 20
B 34
C 36
D 38
Example 2
Brendon has 16 t-shirts. If Nathan had 3 less t-shirts, he would have half as many t-shirts as Brendon.
How many t-shirts does Nathan have?
A 8
B 10
C 11
D 13
Key Rules to remember:
- Read the question carefully. Key words such as 'twice as much' and 'if… will be equal to' reveal important clues that will help you form pictures in your head
- Extract only the necessary information.
- List out the information you have extracted one by one.
- Depict the question visually if that suits you best.
Now it's time to do your assignment.
- Download the assignment question here.
- Print it out or if you want to do it electronically, save it.
- Complete the questions to it.
- Then check the solutions on the video below.
- For the answers in text instead of video, download them here.
