Put out the flags
Problem
Tim and Beth both have a string of flags. They have red flags, white flags, blue flags, and union jacks.
They both counted how many of each colour they had.
Tim's flags are $50$% blue, $35$% red, $10$% white and $5$% union jacks.
Beth's flags are $40$% blue, $32$% red, $20$% white and $8$% union jacks.
They both have as few flags as is possible with those percentages.
Who has the most flags?
Who has the most red flags?
Who has the most blue flags?
How many union jacks do they have between them?
Getting Started
They must have a whole number of flags!
Tim could have $100$ flags but could he have less than $100$ flags?
$50$% of Tim's flags are blue, what does this tell you about the number of flags Tim must have?
As $35$% of Tim's flags are red, what does this tell you about the number of flags Tim must have?
It might help to be able to write $50$% and $35$% as fractions.
Student Solutions
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 |
For each of these we then need toknow the total number of flags :
| 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 |