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Word Problems Involving

Linear Inequalities

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Example 1:

Suppose you have PhP 500 to spend and want to purchase some CDs that cost PhP 200 and/or some cassettes that cost PhP 100. If x represents the number of CDs and y represents the number of cassettes, what are the different ways for you to spend the money?

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Example 1:

Given: PhP 500Cds at PhP 200 eachCassettes at PhP 100 each

Inequalities:

x ≥ 0 and y ≥ 0

200x + 100y ≤ 500 Write as an inequality.

2x + y ≤ 5 Simplify the equation by dividing both sides by 100.

2x + y ≤ 5

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Example 1:Express in slope-intercept form:

2x + y 5 y -2x + 5

y ≤ -2x + 5

m=-2 (0,5)

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Example 1:

y ≤ -2x + 5

m=-2

(0,5)

y

x

5

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3

2

1

1 2

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Example 2:

The Toyota Co. has a daily production quota of $100,000 worth of cars. They produce two types of cars. Their compact model (x) is valued $10,000 and their luxury car (y) is valued at $20,000.

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Example 2:

Write the equation that describes the

production quota. System of inequalities:

x ≥ 0 y ≥ 0

10,000x + 20,000y ≥ 100,000

x + 2y ≥ 10

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Example 2:A. On April 6, the factory produced

5 compacts and 2 luxury cars. Was the company above, below or on target with their quota? Write the equation or inequality that contains this point.Substitute (5,2) to the original inequality.

x + 2y ≥ 10 below the quota

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Example 2:

B. On August 31, the factory produced 9 compacts and 2 luxury cars. Was the company above, below or on target with their quota? Write the equation or inequality that contains this point.

Substitute (9,2) to the original inequality.

x + 2y ≥ 10 above the quota

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Example 2:

C. On December 11, the factory produced 6 compacts and 2 luxury cars. Was the company above, below or on the target with their quota? Write the equation or inequality that contains this point.Substitute (6,2) to the original inequality.x + 2y ≥ 10

on target

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Take note:

X is not more than 8.

x ≤ 8 Y is at most 15.

y ≤ 15 X is at least 17.

x ≥ 17