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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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.