### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

### Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Weekly Problem 2 - 2014

##### Stage: 3 and 4 Challenge Level:

Let $a$ be my weight, $b$ be the baby's weight and $c$ be the nurse's weight.

We have
\begin{align} a+b&=78\\ b+c&=69\\ a+c&=137\;. \end{align}
We can add all three equations together like this:
$$(a+b)+(b+c)+(a+c)=78+69+137\;.$$
It follows that $2(a+b+c)=284$ and hence $a+b+c=142$. So the combined weight is $142\;\mathrm{kg}$.

For an extra challenge can you find the weights of each person?

This problem is taken from the UKMT Mathematical Challenges.

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