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Multiplication Mistake

Age 11 to 14 Short Challenge Level:

Answer: 22

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.