Example 1 The total cost of 5 textbooks and 4 pens is $ 32.00; the total cost of 6 other books of the same text and 3 pens is $ 33.00. Find the cost of each item. Solution: Let x = the cost of a book in dollars, y = the cost of a pen in dollars. Depending on the problem we obtain the two equations: 5x+4y =32 6x+3y=33 Example 2 I have $ 120.00 in 33 tickets at $ 5 and $ 2. How many tickets are $ 5 and how many $ 2? Solution: Let x = the number of tickets of $ 2 and y = the number of tickets $ 5. Under the terms: x + y = 33. Depending on the problem we obtain the two equations: x+y=33 2x+5y=133

For example 1, each text book costs $4 and each pen costs $3.

For example 2, 18 $5 tickets were sold and 15 $2 tickets were sold.

Explanation:

Example 1:

let T = number of text books

let P = number of pens

5T + 4P = 32

6T + 3P = 33 (we can start by dividing this equation by 11)

5T + 4P = 32

2T + 1P = 11 (now lets multiply be -4)

5T + 4P = 32

-8T - 4P = -44 (now we add)

-3T = -12

T = -12 / 3 = 4

P = (2 X 4) + P = 11

P= 11 - 8 = 3

Example 2:

let C = cheap tickets

let E = expensive tickets

C + E = 33  ⇒   C = 33 - E (and now we can replace)

2C + 5E = 120

2(33 - E) + 5E = 120

66 - 2E + 5E = 120

66 + 3E = 120

3E = 120 - 66 = 54

E = 54 / 3 = 18

C = 33 - 18 = 15

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