6757
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2011-02-01T00:00:01
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<p>In Miss Quaffley's class, the girls make up more than $45$% of the pupils, but less than $50$%. What is the smallest possible number of girls in her class?<br></br>
<br></br>
If you liked this problem, <a href="http://nrich.maths.org/public/viewer.php?obj_id=1283&part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p>
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Let $c$ denote the size of the class and $g$ denote the number of
girls. We want $0.45c< g< 0.5c\Leftrightarrow 0.45<
\frac{g}{c}< 0.5$.<br></br>
<br></br>
If we try $g=1$ there is no such $c$, since if $c=1$ or $c=2$,
$\frac{g}{c}$ is too large, and if $c> 2$, $\frac{g}{c}$ is too
small.<br></br>
<br></br>
Similarly for $g=2$, $3$ or $4$. However for $g=5$ setting $c=11$
leads to $\frac{g}{c}=\frac{5}{11}=\frac{500}{11}$%
$=(\frac{440}{11}+\frac{60}{11})$%
$=(40+\frac{55}{11}+\frac{5}{11})$% $=45\frac{5}{11}$%.<br></br></mdoxml>
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Weekly Problem 3 - 2010
Fractions, Decimals, Percentages, Ratio and Proportion
Percentages
Fractions, Decimals, Percentages, Ratio and Proportion
Calculating with percentages