Mathland Election

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.

One or Both

Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?

Put Out the Flags

Stage: 3 Challenge Level:

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.

The second part of the problem:
Out of every $20$ flags Tim would have $1$ union jack.
Out of every $25$ flags Beth would have $2$ union jacks.
So first we thought about how many different ways you could make $10$ 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
That is assuming that they both have some flags!