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
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Ответ:
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
Ответ:
The percent of increase is 1%. To figure this out, simply reason that 1% of $100 is $1. Therefore, because $300 is a threefold increase, 1% would be $3.