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Answer: $21$
Working backwards
$\times 4 \rightarrow -30\rightarrow \times2 \rightarrow -10\rightarrow$ answer 2 digits
$\div4\leftarrow +30 \leftarrow \div2 \leftarrow + 10 \leftarrow$ answer 2 digits
Answer 2 digits, largest possible $99$
So the largest possible choice is 21.
Using algebra
Brian chooses be $b$
Multiply by $4$ and subtract $30$: $4b-30$
multiply this by $2$ and subtract $10$: $2(4b-30)-10 = 8b-70$
Answer two digits, largest possible $99$
If Brian got $99$:
$8b-70=99\\
\Rightarrow 8b=169\\
\Rightarrow b = 21.125$
So $b\le21.125$ and $b$ is an integer so $b=21$
Brian's Number
Age 14 to 16
ShortChallenge Level 
Answer: $21$
Working backwards
$\times 4 \rightarrow -30\rightarrow \times2 \rightarrow -10\rightarrow$ answer 2 digits
$\div4\leftarrow +30 \leftarrow \div2 \leftarrow + 10 \leftarrow$ answer 2 digits
Answer 2 digits, largest possible $99$
| Answer | $+10$ | $\div2$ | $+30$ | $\div4$ |
| $99$ | $109$ | $54.5$ | $84.5$ | Not an integer |
| $98$ | $198$ | $54$ | $84$ | $21$ good |
So the largest possible choice is 21.
Using algebra
Brian chooses be $b$
Multiply by $4$ and subtract $30$: $4b-30$
multiply this by $2$ and subtract $10$: $2(4b-30)-10 = 8b-70$
Answer two digits, largest possible $99$
If Brian got $99$:
$8b-70=99\\
\Rightarrow 8b=169\\
\Rightarrow b = 21.125$
So $b\le21.125$ and $b$ is an integer so $b=21$
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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