### Inequalities

A bag contains 12 marbles. There are more red than green but green and blue together exceed the reds. The total of yellow and green marbles is more than the total of red and blue. How many of each colour there are in the bag?

### What's it Worth?

There are lots of different methods to find out what the shapes are worth - how many can you find?

### Turnips

Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

# Multiplication Mistake

##### Age 11 to 14 Short Challenge Level:

Using algebra
Let the number that Jane multiplied by be called $n$. Then $54n$ is $198$ more than $45n$.

So $54n=45n+198$, so $54n-45n=198$, so $9n=198$, so $n=198\div9=22$.

Trying different numbers and using proportion
10:    54$\times$10 = 540, 45$\times$10 = 450     difference = 90 which is 9$\times$10

20:   54$\times$20 = 1080, 45$\times$20 = 900    difference = 180 which is 9$\times$20

Need difference of 198 = 9$\times$22, so try 22

22:   54$\times$22 = 1188, 45$\times$20 = 990    difference = 192

Why is it 9 times the number? Because 54 $-$ 45 = 9

You can find more short problems, arranged by curriculum topic, in our short problems collection.