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Aditya sent us a very well explained solution to this problem:
Tim has $50$% blue, $35$% red, $10$% white and $5$% union jacks.
Beth has $40$% blue, $32$% red, $20$% white and $8$% union jacks.In fractions, this is:
T = $\frac{1}{2}$ blue, $\frac{7}{20}$red, $\frac{1}{10}$ white & $\frac{1}{20}$ union jack.
= $\frac{10}{20}$ blue, $\frac{7}{20}$ red, $\frac{2}{20}$ white and $\frac{1}{20}$ union jacks.
Therefore Tim has $20$ flags .
B = $\frac{2}{5}$ blue, $\frac{8}{25}$ red, $\frac{1}{5}$ white & 2/25 $\frac{2}{25}$ union jacks.
= $\frac{10}{25}$ blue, $\frac{8}{25}$ red, $\frac{5}{25}$ white and $\frac{2}{25}$ union jacks.
Therefore Beth has $25$ flags .Now, we know that Beth has more flags than Tim. Beth has one more red flag, and both have the same number of blue flags. Between them, they have $3$ union jacks.
Tim | Beth |
8 | 2 |
6 | 4 |
4 | 6 |
2 | 8 |
Tim | Beth | Tim has this number of flags | Beth has this number of flags | Total number of flags |
8 | 2 | 160 | 25 | 185 |
6 | 4 | 120 | 50 | 170 |
4 | 6 | 80 | 75 | 155 |
2 | 8 | 40 | 100 | 140 |