# Math Help - A little help with percentages!

1. ## A little help with percentages!

Hello Maths people... I need to answer this problem for tomorrow but I'm just completely stuck. Any genius out there please??

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, 25% red, 10% white and 15% union jacks.
Beth's flags are 40% blue, 24% red, 20% white and 16% union jacks.
They both have as few flags as possible with those percentages.

1- Who has the most flags?
2 - Who has the most red flags?
3 - Who has the most blue flags?
4 - How many union jacks do they have between them?

2. I will just help with number 1, I figure that solves everything

Tim's flags are 50% blue, 25% red, 10% white and 15% union jacks.
Beth's flags are 40% blue, 24% red, 20% white and 16% union jacks.

Dealing with Tim, all his flags must have integer values
$White=\frac{T}{10}$, hence T must be a multiple of 10
$Union Jack=\frac{3T}{20}$, hence T must be a multiple of 20.
$Blue=\frac{T}{2}$, hence T must be a multiple of 2
$Red=\frac{T}{4}$, hence T must be a multiple of 4

Find the L.C.M., which is 20 so Tim has 20 flags

For Beth
$White=\frac{B}{5}$, B multiple of 5
$Union=\frac{4B}{25}$ B multiple of 25
$Blue-\frac{2B}{5}$ B multiple of 5
$Red=\frac{6B}{25}$ B multiple of 25.

L.C.M.=25
Beth has 25 flags

Everything else is just using the given data to solve