Patterns And Relations Worksheet - Grade 7 Page 19
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46A Solution
a) The cost of renting a room is $35.
This does not depend on how many people come.
The cost of food is $4 per person.
If 5 people come, the cost of food in dollars is: 4
5
20
If n people come, the cost of food in dollars is: 4
n, or 4n
So, n is related to 35
4n.
b) To find the cost for 10 people, substitute n
10 into 35
4n.
35
4n
35
4(10)
4(10) means 4
10.
35
40
75
The party will cost $75.
To find the cost for 15 people, substitute n
15 into 35
4n.
35
4n
35
4(15)
35
60
95
The party will cost $95.
c) If the cost of food doubles, Mr. Prasad will pay $8 per person.
If n people come, the cost for food, in dollars, is 8n.
For n people, the cost of the party, in dollars, is now 35
8n.
If 10 people come, the cost is now:
35
8n
35
8(10)
35
80
115
The party will cost $115.
This is an increase of $115
$75
$40.
The answer makes sense because the cost is now $4 more per person.
So, the extra cost for 10 people would be $4
10, or $40 more.
History
The word “algebra” comes from the
Arabic word “al-jabr.” This word appeared
in the title of one of the earliest algebra
texts, written around the year 825 by
al-Khwarizmi. He lived in what is
now Uzbekistan.
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UNIT 1: Patterns and Relations
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