Ratios and Proportions

1
Ratios and Proportions
Chapter 3
2
After completing this chapter, you will be able
to

• Set up and manipulate ratios
• Set up and solve proportions
• Use proportions to allocate or prorate an
  amount on a proportionate basis
• Use quoted exchange rates to convert between
  currencies
• Relate currency exchange rate movement to
  currency appreciation or depreciation
• Interpret and use index numbers

3
Expressing a Ratio in Equivalent Forms
Colleen, Heather and Marks partnership interests
in Creative Crafts are in the ratio of their
capital contributions of 7800, 5200 and 6500
respectively. What is the ratio of Colleens to
Heathers to Markss partnership interest?
Ratio with the given terms in the colon notation
7800 5200 6500
78 52 65
Equivalent ratio (each term divided by 100)
Equivalent ratio with lowest terms (after
division by 52)
1.5 1 1.25
4
The ratio of the sales of Product X to the sales
of Product Y is 43 The sales of product X in
the next month are forecast to be 1800. What
will be the sales of product Y if the sales of
the two products maintain the same ratio?
Cross - multiply
Divide both sides of the equation by 4
4Y 1800 3
13500
5
A 560-bed hospital operates with 232 registered
nurses and 185 other support staff. The hospital
is about to open a new 86-bed wing. Assuming the
same proportionate staffing levels, how many more
nurses and support staff will need to be hired?

560n 23286
560s 18586
560n 19 952
560s 15 910
n 19 952 / 560
s 15 910 / 560
28.41
35.63
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Percent Change
If 1000 grows to 2500, find the percent change.
1000 ___?___ 2500
(/100) 1.0 ? __ ?
initial value Change Final Value
1500 ? 1000
1.0 ? 1500 1.0 / 1000 1.5 150
increase
7
Rate of Percent Increase
change Difference Base
Difference between old and new sales
change 1,500 1,000
Old sales
1.5 or 150 Increase
8
Percent Change
If 15oz. of fruit shrinks to 3 oz., find the
percent change.
_ 15 __?___ 3
(/100) 1.0 - ? __ ?
initial value - Change Final Value
-12 ? 15 1.0 ? -12 1.0 / 15
-0.80 -80
decrease
9
Rate of Percent Decrease
Old
New
change Difference Base
Difference between old and new weight
change -12 15
Old Weight
.80 or 80 Decrease
3 oz.
15 oz.
10
Currency Exchange
11
Currency Cross Rates (noon April 9, 1999
Toronto,) Per C Per US Per Per DM Per
Per Sw fr Canada dollar (C) ? 1.5020 2.4136
0.8282 0.012410 1.0129 US dollar
(US) 0.6658 ? 1.6069 0.5514 0.008262 0.6744 Bri
tish pound () 0.4143 0.6223 ? 0.3431 0.005142 0.4
197 German mark(DM) 1.2074 1.8136 2.9143 ? 0.014
984 1.2230 Japanese yen () 80.58 121.03 194.49
66.74 ? 81.62 Swiss franc (Sw
fr) 0.9873 1.4829 2.3829 0.8177 0.012252 ? Frenc
h franc (Fr fr) 4.0486 6.0810 9.7717 3.3530 0.0502
43 4.1008 Euro () 0.6173 0.9272 1.4900 0.5113 0
.007661 0.6253 0.1525
12
Using the exchange rates given, calculate the
number of yen that C500 could purchase.
We can use either - lets use the second one
Cross - multiply
C500 could purchase 40,290
13
Using the exchange rates given, calculate the
number of Canadian dollars that 5000 could
purchase.
We can use either - lets use the first one
Cross - multiply
5000 could purchase C62.05
14
How much will it cost in Canadian dollars to
purchase US500 of currency at a bank that
charges 1.5 commission on the transaction? Assume
C1.510 US1.00
Cross - multiply
Now calculate the commission
C575.50 0.015 8.63
It cost C575.50 C8.63 C592.76 to buy 500
US.
15
Gasoline sold for C0.659 per litre in Vancouver
and US1.39 per gallon in Seattle. How much
cheaper (based on the Vancouver price) was gas in
Seattle? (1 US gallon 3.785 litres)(C1.5020US
1.00)
Step 1 Calculate the cost in Canada for the
equivalent of 1 gallon of gas.
3.785 litres ? C0.659 per litre C2.494
Step 2 Convert US1.39 to C.
Cross - multiply
Step 3 Calculate the difference between the
Steps 1 and 2 results.
A US gallon was C2.494 C2.088 C0.41
cheaper in Seattle.