WRITING LINEAR SYSTEMS FROM THE GIVEN SITUATIONS

Example 1 :

A store sells a 1-L can of paint for $9.60 and a 4-L can of paint for $20.80. The store has 140 cans of paint, for a total selling price of $2206.40.Write a linear system that models this situation.

Situation :

Let x be the number of 1-L cans and y be the number of 4-L cans.

Given : The store has 140 cans of paint.

x + y = 140

Cost of one 1-L can = $9.60

Cost of x number of 1-L cans = 9.6x

Cost of one 4-L can = $20.80

Cost of y number of 4-L cans = 20.6x

Given : The store has 140 cans of paint, for a total selling price of $2206.40.

9.6x + 20.6y = 2206.4

The system of linear equations which represents the given situation :

x + y = 140

9.6x + 20.6y = 2206.4

Example 2 :

Tickets for the school play cost $8 for an adult and $5 for a student. The total revenue for one performance was $1122, with 32 more students than adults in the audience.

a) Write a linear system that models this situation.

b) Find the number of adult tickets and student tickets sold.

Situation :

Let a be the number of adult tickets and s be the number of student tickets.

Given : There are 32 more students than adults in the audience.

s = a + 32

Cost of one adult ticket = $8

Cost of a number of adult tickets = 8x

Cost of one student ticket = $5

Cost of s number of ticket tickets = 5s

Given : The total revenue for one performance was $1122.

8a + 5s = 1122

The system of linear equations which represents the given situation :

s = a + 32 ----(1)

8a + 5s = 1122 ----(2)

Substitute s = a + 32 in (2).

8a + 5(a + 32) = 1122

8a + 5a + 160 = 1122

13a + 160 = 1122

Subtract 160 from both sides.

13a = 962

Divide both sides by 13.

a = 74

Substitute a = 74 in (1).

s = 74 + 32

s = 106

Therefore,

number of adult tickets sold = 74

number of student tickets sold = 106

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