# Equations and Formulae - Stage 4

### Terminology

##### Stage: 4 Challenge Level:

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

### Arithmagons

##### Stage: 3 Challenge Level:

Can you find the values at the vertices when you know the values on the edges?

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### Matchless

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

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

### Golden Thoughts

##### Stage: 4 Challenge Level:

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.

### Which Is Cheaper?

##### Stage: 4 Challenge Level:

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

### How Old Am I?

##### Stage: 4 Challenge Level:

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

### Which Is Bigger?

##### Stage: 4 Challenge Level:

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

### Fair Shares?

##### Stage: 4 Challenge Level:

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

### Training Schedule

##### Stage: 4 Challenge Level:

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

### CD Heaven

##### Stage: 4 Challenge Level:

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

### Multiplication Arithmagons

##### Stage: 4 Challenge Level:

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

### System Speak

##### Stage: 4 and 5 Challenge Level:

Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6

### Equations and Formulae Stage 4 - Short Problems

##### Stage: 4

A collection of short Stage 4 problems on equations and formulae.

### Square to a Rectangle

##### Stage: 4 Short Challenge Level:

Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?

### Table Total

##### Stage: 4 Short Challenge Level:

Can you find the sum of all of the numbers in the table?

### Symmetric Reasoning

##### Stage: 4 Challenge Level:

Can you sum up the solutions to this equation?