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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 |
$3$ | $63$ | $66$ |
$8$ | $60$ | $68$ |
$13$ | $57$ | $70$ |
$18$ | $54$ | $72$ |
$23$ | $51$ | $74$ |
$28$ | $48$ | $76$ |
$33$ | $45$ | $78$ |
$38$ | $42$ | $80$ |
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.