COMPARING RATE TO ONE ANOTHER

To understand why we learn this concept, let us consider the following situation. 

When we are in shop, we find two deal as follows :

(i)  500 g of detergent costing $3.50

(ii)  750 g detergent costing $5.40

decide which is the better deal.

To properly compare prices, we need to convert the cost of an item into a rate called unit rate.

Consider the following grocery items and decide which is the better value for money:

Question 1 :

Answer :

By choosing small box,

Cost of 300 g of corn flakes  =  $2.15 

=  215 cents

Cost of 1 gram  =  215/300

=  0.716 cents

By choosing large box,

Cost of 500 g of corn flakes  =  $3.29

=  329 cents

Cost of 1 gram  =  329/500

=  0.658 cents

0.716 > 0.658

So, choosing 500 g corn flakes is better deal.

Question 2 :

Answer :

By choosing 6 pack,

Cost of 6 towels  =  $2.99

=  299 cents

Cost of 1 towel  =  299/6

=  49.83

By choosing 4 pack,

Cost of 4 towels  =  $1.79

=  179 cents

Cost of 1 towel  =  179/4

=  44.75

49.83 > 44.75

So, choosing 4 pack is better deal.

Question 3 :

Answer :

By choosing 2 liters can

Cost of 2 liters of milk  =  $3.89

=  389 cents

Cost of 1 liter of milk  =  389/2

=  194.5 cents

Dividing by 100

Cost of 1 liter of milk  =  $1.945

By choosing 600 ml can

Cost of 600 ml milk  =  $2.19

=  219 cents

Cost of 1 ml of milk  =  219/600

Cost of 1000 ml milk (or) Cost of 1 liter milk 

=  (219/600)⋅1000

=  365 cents

Dividing by 100

Cost of 1 liter of milk  =  $3.65

3.65 > 1.945

So, choosing 2 L milk can is the better deal.

Question 4 :

Answer :

By choosing 10 m pack

Cost of 10 meter ribbon  =  $4.20

=  420 cents

Cost of 1 meter ribbon  =  420/10

=  42 cents

Dividing by 100

Cost of 1 meter ribbon  =  $ 0.42

By choosing 8 m pack

Cost of 8 meter ribbon  =  $3.60

=  360 cents

Cost of 1 meter ribbon  =  360/8

=  45 cents

Dividing by 100

Cost of 1 meter ribbon  =  $ 0.45

0.42 < 0.45

So, choosing 10 meter ribbon is the better deal.

Question 5 :

Answer :

By choosing 5 liter can

Cost of 5 liter paint  =  $65

Cost of 1 liter paint  =  65/5

=  $13

By choosing 2 liter can

Cost of 2 liter paint  =  $31

Cost of 1 liter paint  =  31/2

=  $15.50

13 < 15.50

So, choosing 5 liter can is the better deal.

Question 6 :

Answer :

By choosing 25 kg pack

Cost of 25 kg potatoes  =  $35

Cost of 1 kg potato  =  35/25

=  $1.4

By choosing 10 kg pack

Cost of 10 kg potatoes  =  $16.50

Cost of 1 kg potato  =  16.50/10

=  $1.650

1.650 > 1.4

So, choosing 20 kg potato is the better deal.

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