Challenge Level

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 $n=198\div9=22$.

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

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