# 10.6.1. Linear Inequalities

You decided to spend less thanLE to buy cashews and pistachios for a trip. Using the figure below, which illustrates the relation between the number of kilograms of cashews and pistachios that you can buy, find out the price of a kilogram of each.

• AcashewsLE, pistachiosLE
• BcashewsLE, pistachiosLE
• CcashewsLE, pistachiosLE
• DcashewsLE, pistachiosLE

### Example

You decided to spend less thanLE to buy cashews and pistachios for a trip. Using the figure below, which illustrates the relation between the number of kilograms of cashews and pistachios that you can buy, find out the price of a kilogram of each.

### Solution

The boundary line passes through the points and , so calculate its slope, or , as follows:

The line's -intercept, or , is 4, so in slope-intercept form, or , the line's equation is . Add to both sides to get . Since you decided to spend less than to buy cashews and pistachios, the constant on the right side of the equation should be 204. This means that both sides of the equation should be multiplied by as follows:

Therefore, the inequality that represents this situation is , with being the number of kilograms of cashews you purchase, and being the number of kilograms of pistachios. Since is the total cost of cashews, and is the total cost of pistachios, cashews must cost per kilogram, and pistachios must cost per kilogram.

0
correct
0
incorrect
0
skipped