### Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

### Balancing 1

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

### Balancing 2

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

# Oh for the Mathematics of Yesteryear

##### Stage: 3 Challenge Level:

Correct solutions were received from Mary (Birchwood Community High School) and Chor Kiang. Well done.

### Part 1

First, find the total ounces of bread.
$600 \times35 \times24$ ounces $= 504000$ ounces

Now, find the new number of men-shares needed.
$4800 \times45 = 216000$

Divide $504000$ ounces by $216000$ to get $2\frac{1}{3}$ ounces a day.

Hence, each man must only eat $2\frac{1}{3}$ ounces of bread a day.

### Part 2

$£14 10\text{s} = 290\text{s}$

$£5 \; 8\text{s } 9 \text{d} = 108.75$ shillings

Weight (cwt)   Distance (miles) Amount (shillings)
$60$ can be transported for $20$ for $290$
$1$ can be transported for $20$ for $\frac{290}{60} = \frac{29}{6}$
$1$ can be transported for $30$ $\frac{29}{6}\times\frac{30}{20}= 7.25$
$\frac{1}{7.25}$ can be transported for $30$ $1$
$\frac{1}{7.25}\times 108.75$ can be transported for $30$ $108.75$

Since $\frac{108.75}{7.25} = 15$

$15$ cwt can be carried for $30$ miles at a cost of $£5 \; 8\text{s } 9 \text{d}$