A student wrote the equation 4(x+5.5)=3(1.5x+4.75) to represent the problem shown. Find her mistake and correct it.
1 answer:
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Answer:
We know that:
Price of a taco = $4
Price of a burrito = $6.50
x = number of tacos sold
y = number of burritos sold.
We must have that:
x + y ≤ 150 (Because she only has supplies to make 150 tacos or burritos, but she can sell less than that)
And also we know that she must sell at least $780, then:
x*$4 + y*$6.50 ≥ $780
Now we found the system of inequalities:
x + y ≤ 150
x*$4 + y*$6.50 ≥ $780
To solve it graphically, we just need to find each one of the region solutions for each equation, and the intersection of these regions will be the solution for the system.
To graph them may be easier to write them as lines, you can do it as follows:
y ≤ 150 - x
y ≥ ($780 - x*$4)/$6.50
in the first equation, we will shade the area below the line, and in the second equation, we will shade the area above the line.
You can see the image below.
Where the accepted solutions are the ones in the darker part, and we only restrict this to positive values of x (because of how we defined the variable x)
Then looking at the image, we can see that one solution can be the point
x = 20, y = 120
