250x + 475y ≤ 8000
To graph this inequality, first rewrite it in slope-intercept form:
475y ≤ -250x + 8000
y ≤ (-250/475)x + 16.84
Then, graph the line y = (-250/475)x + 16.84 (note that the slope is negative because as x increases, y decreases).
To determine which side of the line represents the valid solutions, choose a test point not on the line, such as (0,0). Substitute the x and y values into the inequality:
250(0) + 475(0) ≤ 8000
0 ≤ 8000
Since this is true, the valid solutions are below the line. Shade in the region below the line on the graph.
To determine if 14 refrigerators and 10 pianos will overload the truck, substitute x = 14 and y = 10 into the inequality:
250(14) + 475(10) ≤ 8000
3550 + 4750 ≤ 8000
8300 ≤ 8000
This is false, so the truck can carry 14 refrigerators and 10 pianos without overloading.
A truck that can carry no more than 8,000 Ib is being used to transport refrigerators and upright pianos. Each refrigerator weighs 250 Ib and each piano weighs 475 Ib. Write and graph an inquality to shower how many refigerators and how many pianos that truck could carry. Will 14 refrigerators and 10 pianos overload the truck? Explain.
Let x be the number of refrigerators in the truck and y be the number of pianos in the truck. Write an inequality to show how many refrigerators and how many pianos the truck could carry.
(Use integers or simplified fractions for any numbers in the inequality. Do not factor.)
1 answer