The Chocolate Dilemma
To make sure we have a good understanding of proportions, we are going to spend some time calculating modifications to one of our favourite things:
Chocolate!!!
And when we are done with it, we get to eat them! Yum.
The best method to make calculations that are complicated is the data collection method.
Start by writing down everything you know, and labelling it well!
Let's see an example:
A chocolate bar is 18 centimetres long by 7 centimetres wide. A chocolatier wants to make the bar 5 centimetres longer, but keep in in proportion. How wide should the bar be?
Data:
Length of small bar (l) = 18cm
Width of small bar (w) = 7 cm
Length of bigger bar (L) = 23 cm
Width of bigger bar (W) = X
The way to calculate this is to think -- Big is to big as small is to small. That is what makes things proportional -- the relationship between parts.
So, how do you calculate it?
18 = 23 (small length is to big length)
7 = X (small width is to big width)
Cross multiply, and you get 18 X = 161
So, X = 8.94.
Now, let's measure our chocolate bars and figure out what happens if...
Chocolate!!!
And when we are done with it, we get to eat them! Yum.
The best method to make calculations that are complicated is the data collection method.
Start by writing down everything you know, and labelling it well!
Let's see an example:
A chocolate bar is 18 centimetres long by 7 centimetres wide. A chocolatier wants to make the bar 5 centimetres longer, but keep in in proportion. How wide should the bar be?
Data:
Length of small bar (l) = 18cm
Width of small bar (w) = 7 cm
Length of bigger bar (L) = 23 cm
Width of bigger bar (W) = X
The way to calculate this is to think -- Big is to big as small is to small. That is what makes things proportional -- the relationship between parts.
So, how do you calculate it?
18 = 23 (small length is to big length)
7 = X (small width is to big width)
Cross multiply, and you get 18 X = 161
So, X = 8.94.
Now, let's measure our chocolate bars and figure out what happens if...
- We make them 20 centimeters wider - What is the new length?
- We make them 50 centimeters longer - What is the new width?
- We make them 25% bigger - What are the new measures?
- We make them 15% smaller - What are the new measures?
- We make them twice as big - What are the new measures? What is the percentage of increase?
- We make them 10 centimeters wider - what is the percentage of increase?
EAT CHOCOLATEEEEE
