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There are many solutions to this problem. Here is one correct solution received from a student at West Flegg Middle School in Norfolk.
Dee | Dum |
48 | 28 |
32 | 44 |
54 | 22 |
18 | 58 |
61.50 | 14.50 |
20.50 | 55.50 |
39 | 37 |
38 | 38 |
Hence, they share 76 pounds between them.
Year 5 pupils at Sutton High School also found a couple of solutions.
Ewan, from King Edward VII School in Sheffield, used algebra to make sure he found all the possible solutions.
DUM | DEE |
$x$ | $y$ |
$x+\frac{1}{3}y$ | $\frac{2}{3}y$ |
$\frac{1}{2}x+\frac{1}{6}y$ | $\frac{1}{2}x+\frac{5}{6}y$ |
$\frac{5}{6}x+\frac{13}{8}y$ | $\frac{1}{6}x+\frac{5}{8}y$ |
$\frac{5}{24}x+\frac{13}{72}y$ | $\frac{19}{24}x+\frac{59}{72}y$ |
$\frac{53}{72}x+\frac{157}{216}y$ | $\frac{19}{72}x+\frac{59}{216}y$ |
$\frac{53}{108}x+\frac{157}{324}y$ | $\frac{55}{108}x+\frac{167}{324}y$ |
$x$ | $y$ | Total |
$3$ | $63$ | $66$ |
$8$ | $60$ | $68$ |
$13$ | $57$ | $70$ |
$18$ | $54$ | $72$ |
$23$ | $51$ | $74$ |
$28$ | $48$ | $76$ |
$33$ | $45$ | $78$ |
$38$ | $42$ | $80$ |