Begin by finding the discounted cost of both items.
Inequality: 3.10x+2.40y ≤ 20 Graph:
Practice makes perfect
To begin we can determine the discounted cost of both items. It is given that the original cost per gallon of milk is $3.60 and that it is discounted by $0.50. Subtracting gives us the discounted price of milk.
3.60-0.50=$3.10
It's also given that the original cost of meat is $3.00 per pound and that it is discounted 20 %. To determine the discounted price of meat, we will find 20 % of 3.00 and subtract it from 3.00.
3.00- 0.20 * 3.00 = $2.40
Writing an Inequality
Let x represent the number of gallons of milk we buy, while y represents the number of pounds of meat we buy. Therefore, we will pay $3.10* x for the milk and $2.4* y for the meat. Since it is given that we want to spend no more than 20 dollars, we can write the inequality.
3.10x+2.40y ≤ 20
Graphing the Inequality
To graph the inequality, we first have to express it in slope-intercept form. To do so, we will isolate y.
Now that the inequality is written as y ≤ - 1.3x+ 8.3, we can see that the slope of the boundary line is 1.3 and the y-intercept is 8.3. We will use these to graph the boundary line. Since the symbol is ≤ the line will be solid and we will shade the area below the graph.
The graph only makes sense in the first quadrant, since it's impossible to buy a negative amount of meat or milk.
