# 10.6.2. Solving Systems of Linear Inequalities Graphically

A carpenter wants to spend less than 55 pounds; at least 5 of the first type and 7 of the other. Given that the prices of a kilogram of the first and second types are 6 and 9 pounds respectively, state a system of inequalities that represents this situation.

• A, ,
• B, ,
• C, ,
• D, ,

### Example

A carpenter wants to spend less than 55 pounds; at least 5 of the first type and 7 of the other. Given that the prices of a kilogram of the first and second types are 6 and 9 pounds respectively, state a system of inequalities that represents this situation.

### Solution

Suppose is the number of kilograms of the first type purchased, and is the number of kilograms of the second type purchased. The words "at least" indicate that is greater-than-or-equal-to 5 and that is greater-than-or-equal-to 7. Since the first type costs 6 pounds per kilogram, the total number of pounds the carpenter will spend on the first type is . Since the second type costs 9 pounds per kilogram, the total number of pounds the carpenter will spend on the second type is . The words "less than" indicate that the sum of and is less than 55. Thus, the system of inequalities that represents this situation is , , .

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