1. Simultaneous equations

2. Figure out how much a cap costs.
What’s the biggest trick here?

3. If I spend $60 what could I get now?

4. (1) 2c + 1g = $45 (2) c + 3g = $30 multiply by 2
2 caps + 1 pair of glasses = $45
1 cap + 3 pairs of glasses = $30
So 2 caps + 6 pairs of glasses = $60
and so 5 pairs of glasses = $60 - $45
1 pair of glasses = $3 and 1 cap = $21
(1) 2c + 1g = $45
(2) c + 3g = $30 multiply by 2
So 2c + 6g = $60 (2) minus
2c + 1g = $45 (1)
and so 5g = $15
g = $3
1g = $3, 1c = $21

5. Cows and Hens c + h = 50 2h + 4c = 140 legs
On his farm, Joe has 50 animals, all cows and hens.
The 50 animals have 140 legs in total.
How many cows and hens are there?
How could you see the problem? Can we draw these on a number line diagram?
c + h = h + 4c = 140 legs

6. Cows and Hens
(1) c + h = (2) 2h + 4c = 140 legs

7. Cows and Hens
Taking the mathematical model and using geometry we now have
(2x1) 2c + 2h = 100 and (2) 2h + 4c = 140
2h + 4c = (2) minus
2h + 2c = 100 (1)
2c = 40
Therefore, there must be 20 cows and 30 hens.

8. Wetas and Spiders
A museum has a collection of 66 different wetas and spiders.
The wetas and spiders have 484 legs in total.
How may wetas are there and how many spiders are there?

9. Wetas and Spiders
Therefore, there must be 22 wetas and 44 spiders.