Skylar owns a food truck that sells tacos and burritos. She sells each taco for $3 and each burrito for $6. Yesterday Skylar made a total of $600 in revenue from selling a total of 120 tacos and burritos. Graphically solve a system of equations in order to determine the number of tacos sold, x, x, and the number of burritos sold, yy.

She sold 40 tacos and 80 burritos.

Step-by-step explanation:

Let's define the variables:

x = number of tacos sold

y = number of burritos sold

if Skylar sold x tacos, and each taco costs $3, then the total amount she gets is:

$3*x

And if she sold y burritos, and each one costs $6, then the total amount she gets is:

$6*y

combining these two, she has:

$3*x + $6*y

We know that she made a total revenue of $600, then we have the equation:

$3*x + $6*y = $600

We also know that in total, she sold 120 tacos and burritos, then:

x + y = 120

We have the system of equations:

$3*x + $6*y = $600

x + y = 120

To solve this, we need to start by isolating one of the variables in one of the equations, i will isolate x in the second equation:

x = 120 - y

Now we can replace that in the other equation to get

$3*(120 - y) + $6*y = $600

-$3*y + $360 + $6*y = $600

($6 - $3)*y + $360 = $600

$3*y + $360 = $600

$3*y = $600 - $360 = $240

y = $240/$3 = 80

She sold 80 burritos, and we know that:

x + y = 120

x + 80 = 120

x = 120 - 80 = 40

She sold 40 tacos.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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