Example 4

You have $10 to spend on reprints of a picture you took in Pfeiffer Big Sur State Park. You would like to send one copy to at least 12 friends. Small prints cost $.50 and large prints cost $1. Write and graph a system of inequalities to describe the situation. Then determine two possible combinations of print sizes you can buy.

PHOTOGRAPHY

Writing a System of Linear Inequalities

Example 4 Writing a System of Linear Inequalities

SOLUTION

STEP 1 Write a system of inequalities where x is the number of small prints and y is the number of large prints. The number of prints cannot be negative, so you need to include the inequalities and .0x ≥ 0y ≥

0x ≥ The number of small prints cannot be negative.

0 y ≥ The number of large prints cannot be negative.

You want to send prints to at least 12 friends.yx 12+ ≥

You have $10 to spend on the prints.y0.5x 10+ ≤

Writing a System of Linear InequalitiesExample 4

STEP 2 Graph each inequality in the system.

STEP 3 Identify the region thatis common to all of the graphs. This region is shaded blue in the graph shown at the right.

STEP 4 Determine how many of each print size you can buy.

Writing a System of Linear InequalitiesExample 4

ANSWER

Several solutions are possible, such as and as shown at the right. You can buy 10 small prints and 4 large prints, or 16 small prints and 2 large prints.

( )10, 4 ( )16, 2

Guided Practice

9. WHAT IF?In Example 4, suppose you are given an additional $5 to spend on reprints. Graph the new system of inequalities and give two new possible combinations of print sizes you can buy.

for Example 4

Guided Practice for Example 4

ANSWER

Sample answers: , .( )10, 6 ( )11, 2