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you have seen, proportions are powerful tools for solving
As
However, how do you know when a relationship is
problems.
Can you solve every problem with proportions, or
proportional?
only certain kinds of questions involve proportional reasoning?
do
4 – Recognizing proportional
Investigation
relationships
countries provide incentives for their athletes at the Olympics. While
Many
athletes, for example, receive no monetary award for winning medals,
British
countries, such as India, pay their athletes for outstanding performances
some
order to increase their competitive spirit.
in
India, the amount of money earned per gold medal is given below. This is a
In
relationship
proportional
of
Number
medals
gold
Payment
(euros)
Plot the number of gold medals on the x-axis and the payment on the
a
Describe the type of graph obtained.
y-axis.
How much would a person be paid for winning no gold medals? How much
b
a person be paid for winning 10 gold medals? Explain how you
would
Thailand, gold medallists earn US$314 000 to be paid in equal amounts
In
20 years.
over
How much would an athlete be paid each year? Show
c
working.
your
do you multiply by to nd the total money paid in
What
year? This is called the constant of proportionality
any
Find an equation for your graph. Explain how the
g
of proportionality is represented in the
constant
B, C
money paid
Total
(US$)
Recognizing and using proportional reasoning
criteria
2 200 000
3 300 000
4 400 000
5 500 000
found your answers.
Year
d Fill in the table on the right and graph your results.
0
1
e Is this a proportional relationship? Explain.
2
f
3
4
5
10
equation.
20
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1 Ratios and proportions