Michaela has up to $20 to spend on bottled water and orange juice for a group hike. It cost $2 for each bottle of water and $ 4 for each bottle pdf orange juice.
write an inequality statement of this situation?
2x +4y< or equal to 20
Y < or equal to-1/2x +5
once this is graphed I am asked can Michaela buy 5 bottles of water and 7 bottles of orange juice why or why not use the graph to justify your answer. I know the answer is no so how do I justify this answer using the graph?
y </= -(1/2) x + 5
y </= -(1/2) 5 + 5 ??
y </= -2.5 + 5
y</= 2.5
If I buy 5 bottles of water, I can buy no more than 2.5 bottles of oj
the graph is a line
one side is the true region, the other side is the false region
5 water and 7 OJ lies in the false region
To answer whether Michaela can buy 5 bottles of water and 7 bottles of orange juice, we need to check if these values satisfy the inequality. Let's substitute x=5 and y=7 into the inequality:
2x + 4y ≤ 20
2(5) + 4(7) ≤ 20
10 + 28 ≤ 20
38 ≤ 20
Since this statement is not true, it means that the combination of 5 bottles of water and 7 bottles of orange juice exceeds the maximum spending limit of $20. Therefore, Michaela cannot buy 5 bottles of water and 7 bottles of orange juice.
To justify the answer using the graph, you need to plot the line representing the inequality: 2x + 4y ≤ 20.
To graph this equation, first, convert it into the slope-intercept form (y = mx + b), which is in the form y ≤ mx + b. Rearrange the equation:
4y ≤ -2x + 20
Divide both sides by 4 to isolate y:
y ≤ -1/2x + 5
The inequality is already in the form y ≤ mx + b, where m is the slope (-1/2) and b is the y-intercept (5).
Now, to graph this inequality:
1. Start by plotting the y-intercept on the graph, which in this case is (0, 5).
2. Use the slope (-1/2) to find a second point. Since the slope is negative, move one unit to the right and two units down, and mark a point there.
3. Draw a solid line through the two points you marked.
Your graph should now have a line representing the inequality y ≤ -1/2x + 5.
To determine if Michaela can buy 5 bottles of water and 7 bottles of orange juice, locate the point (5, 7) on the graph.
If the point (5, 7) is below or on the line, it means that the solution satisfies the inequality and Michaela can buy 5 bottles of water and 7 bottles of orange juice. However, if the point is above the line, it means that the solution does not satisfy the inequality and Michaela cannot buy that combination.
In this case, when you locate the point (5, 7) on the graph, you will find that it lies above the line. This means that the combination of 5 bottles of water and 7 bottles of orange juice exceeds the maximum cost of $20 that Michaela can spend. Therefore, the answer is no, Michaela cannot buy 5 bottles of water and 7 bottles of orange juice within her budget.