Units Of Measurement And Applications Worksheet Page 35
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442J
The unitary method
The unitary method
The unitary method is used to fi nd the value of a number of items (or variables) by fi rst fi nding the value of one item.
WORKED EXAMPLE 1
The cost of 3 kg of fi sh is $27.87. What is the cost of 5 kg of this fi sh?
Solve
Think
Apply
5 kg cost
As the cost of 3 kg is given, fi nd the cost
First fi nd the cost of 1 unit (in this
= ($27.87 ÷ 3) × 5
of 1 kg by dividing by 3. Then fi nd the cost
case 1 kg) and then multiply by the
= $46.45
of 5 kg by multiplying this result by 5.
required number of units 5 (kg).
EXERCISE 2J
1
The cost of 5 pairs of socks is $18.75. Find the cost of 6 pairs of these socks.
2
If 8 kg of potatoes cost $19.92, what is the cost of 5 kg of potatoes?
3
The cost of 50 m of rope is $63. Find the cost of 20 m of this rope.
WORKED EXAMPLE 2
A discount of 17.5% on a refrigerator results in the price decreasing by $152.25. Find the original price of
the refrigerator.
Solve
Think
Apply
17.5% of the original price = $152.25
Original price
Find 1% of the original
= ($152.25 ÷ 17.5) × 100
1% of the original price
price, then multiply by
= $152.25 ÷ 17.5 = $8.70
= $870
100 to fi nd (100% of) the
∴ 100% of the original price
original price.
= $8.70 × 100 = $870
4
A discount of 18% on a bicycle results in the price decreasing by $179.82. Complete the following to fi nd the
original price of the bicycle.
18% of the original price = $____
1% of the original price = $____ ÷ ____ = $____
∴ 100% of the original price = $____ ×____ = $____
5
At a certain school, 35% of the students travel by bus. If 259 students travel by bus, how many students are
there at the school?
6
Linda and Matthew pay a 15% deposit of $84 000 on their new house. What is the total cost of the house?
7
It is calculated that 2% of the Australian fur seal population dies each year from entanglement in nets or ropes
discarded by fi shers. If approximately 600 seals die each year, estimate the size of the fur seal population.
Chapter 2
Units of measurement and applications
69
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