# 10.6.1. Linear Inequalities

Suppose you decided to spend not more than pounds to buy a snack of peanuts and berries for your trip to the zoo with your family. Given that the price of peanuts is 73 pounds and that of berries is 52 pounds, what is the relation that defines the amounts of each that you'll buy?

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### Example

Suppose you decided to spend not more than pounds to buy a snack of peanuts and berries for your trip to the zoo with your family. Given that the price of peanuts is 73 pounds and that of berries is 52 pounds, what is the relation that defines the amounts of each that you'll buy?

### Solution

Suppose is the number of kilograms of peanuts you purchase, and is the number of kilograms of berries you purchase. Since peanuts cost 73 pounds per kilogram, the total number of pounds you will spend on peanuts is . Since berries cost 52 pounds per kilogram, the total number of pounds you will spend on berries is . The words "not more than" indicate that the inequality that represents this situation should contain a less-than-or-equal-to sign, so the correct inequality is .

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